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We compare tame actions in the category of schemes with torsors in the category of log schemes endowed with the log flat topology. We prove that actions underlying log flat torsors are tame. Conversely, starting from a tame cover of a regular scheme that is an fppf torsor on the complement of a divisor with normal crossings, it is possible to build a unique log flat torsor that dominates this cover. In brief, the theory of log flat torsors gives a canonical approach to the problem of extending torsors into tame covers. [ABSTRACT FROM AUTHOR]

For any almost-simple group G over an algebraically closed field k of characteristic zero, we describe the automorphism group of the moduli space of semistable G -bundles over a connected smooth projective curve C of genus at least 4. The result is achieved by studying the singular fibers of the Hitchin fibration. As a byproduct, we provide a description of the irreducible components of two natural closed subsets in the Hitchin basis: the divisor of singular cameral curves and the divisor of singular Hitchin fibers. [ABSTRACT FROM AUTHOR]

We study moduli stacks of principal C ∗ -bundles over nodal complex algebraic curves and determine their rational cohomology algebras in terms of Chern classes. [ABSTRACT FROM AUTHOR]

In this paper, we study the action of diamond operators on Hilbert modular forms with coefficients in a general commutative ring. In particular, we generalize a result of Chai on the surjectivity of the constant term map for Hilbert modular forms with nebentype to the setting of group ring valued modular forms. As an application, we construct certain Hilbert modular forms required for Dasgupta–Kakde's proof of the Brumer–Stark conjecture at odd primes. Since the forms required for the Brumer–Stark conjecture live on the non-PEL Shimura variety associated to the reductive group G = Res F / Q (GL 2) , as opposed to the PEL Shimura variety associated to the subgroup G ∗ ⊂ G studied by Chai, we give a detailed explanation of theory of algebraic diamond operators for G, as well as how the theory of toroidal and minimal compactifications for G may be deduced from the analogous theory for G ∗ . [ABSTRACT FROM AUTHOR]

In this paper we consider the Br = Br ′ question for classifying stacks by various group schemes. These are algebraic stacks that do not necessarily admit a finite flat cover by a scheme for which Br = Br ′ holds, hence are not amenable to the usual argument of pushing forward a twisted vector bundle. We provide two classes of examples satisfying Br ≠ Br ′ that do not arise from the scheme case. Communicated by Tony Varilly-Alvarado [ABSTRACT FROM AUTHOR]

We consider a Deligne–Mumford stack $X$ which is the quotient of an affine scheme $\operatorname {Spec}A$ by the action of a finite group $G$ and show that the Balmer spectrum of the tensor triangulated category of perfect complexes on $X$ is homeomorphic to the space of homogeneous prime ideals in the group cohomology ring $H^*(G,A)$. [ABSTRACT FROM AUTHOR]

One fundamental consequence of a scheme $X$ being proper is that the functor classifying maps from $X$ to any other suitably nice scheme or algebraic stack is representable by an algebraic stack. This result has been generalized by replacing $X$ with a proper algebraic stack. We show, however, that it also holds when $X$ is replaced by many examples of algebraic stacks which are not proper, including many global quotient stacks. This leads us to revisit the definition of properness for stacks. We introduce the notion of a formally proper morphism of stacks and study its properties. We develop methods for establishing formal properness in a large class of examples. Along the way, we prove strong $h$ -descent results which hold in the setting of derived algebraic geometry but not in classical algebraic geometry. Our main applications are algebraicity results for mapping stacks and the stack of coherent sheaves on a flat and formally proper stack. [ABSTRACT FROM AUTHOR]

We extend the stable motivic homotopy category of Voevodsky to the class of scalloped algebraic stacks, and show that it admits the formalism of Grothendieck's six operations. Objects in this category represent generalized cohomology theories for stacks like algebraic K-theory, as well as new examples like genuine motivic cohomology and algebraic cobordism. These cohomology theories admit Gysin maps and satisfy homotopy invariance, localization, and Mayer–Vietoris. For example, we deduce that homotopy K-theory satisfies cdh descent on scalloped stacks. We also prove a fixed point localization formula for torus actions. Finally, the construction is contrasted with a "lisse-extended" stable motivic homotopy category, defined for arbitrary stacks: we show for example that lisse-extended motivic cohomology of quotient stacks is computed by the equivariant higher Chow groups of Edidin–Graham, and we also get a good new theory of Borel-equivariant algebraic cobordism. Moreover, the lisse-extended motivic homotopy type is shown to recover all previous constructions of motives of stacks. [ABSTRACT FROM AUTHOR]

We study the various arithmetic and geometric Frobenius morphisms on the moduli stack of principal bundles over a smooth projective algebraic curve and determine explicitly their actions on the l -adic cohomology of the moduli stack in terms of Chern classes. [ABSTRACT FROM AUTHOR]

Let X be a fs logarithmic scheme which admits a strict closed embedding into a logarithmically smooth scheme Y over a field k of characteristic zero. We construct a simple and fast procedure to make a functorial logarithmic resolution of X, where the end result is, in particular, a stack-theoretic modification X' → X such that X' is logarithmically smooth over k. In particular, if X is a finite-type k-scheme embedded in a smooth k-scheme Y, the procedure not only shares the same desirable features as the “dream resolution algorithm” of Abramovich–Temkin–W lodarczyk [Functorial embedded resolution via weighted blowings up, arxiv: 19'6.'71'6] but also accounts for a key feature of Hironaka’s Main Theorem I in [Resolution of singularities of an algebraic variety over a field of characteristic zero. I, Ann. of Math. 79 (1964), no. 1, 1'9–2'3] which was not addressed in the Abramovich–Temkin–W lodarczyk paper. As a consequence, we recover a different and simpler approach to Hironaka’s resolution of singularities in characteristic zero. [ABSTRACT FROM AUTHOR]

Given an ideal I on a variety X with toroidal singularities, we produce a modification X' → X, functorial for toroidal morphisms, making the ideal monomial on a toroidal stack X'. We do this by adapting the methods of [Wło05], discarding steps which become redundant. We deduce functorial resolution of singularities for varieties with logarithmic structures. This is the first step in our program to apply logarithmic desingularization to a morphism Z → B, aiming to prove functorial semistable reduction theorems. [ABSTRACT FROM AUTHOR]

These lectures give a detailed and almost self-contained introduction to algebraic stacks. A great part of the paper is devoted to preliminary technical topics, both from category theory (like Grothendieck topologies, fibred categories and stacks) and algebraic geometry (like faithfully flat descent). All this machinery is finally used to present the definition and some basic properties first of algebraic spaces and then of algebraic stacks.

In this paper we show that the moduli stacks of Bridgeland semistable objects on smooth projective 3-folds are quasi-proper algebraic stacks of finite type if they satisfy the Bogomolov–Gieseker (BG for short) inequality conjecture proposed by Bayer, Macrì and the second author. The key ingredients are the equivalent form of the BG inequality conjecture and its generalization to arbitrary very weak stability conditions. This result is applied to define Donaldson–Thomas invariants counting Bridgeland semistable objects on smooth projective Calabi–Yau 3-folds satisfying the BG inequality conjecture, for example on étale quotients of abelian 3-folds. [ABSTRACT FROM AUTHOR]

Abstract We construct a presentation for the Grothendieck group of Deligne–Mumford stacks over a field of characteristic zero. The generators for this presentation are smooth, proper Deligne–Mumford stacks and the relations are expressed in terms of stacky blow-ups. In the process we prove a version of the weak factorization theorem for Deligne–Mumford stacks. [ABSTRACT FROM AUTHOR]

Abstract This paper studies two approaches to formalize helping in wait-free implementations of shared objects. The first approach is based on operation valency , and it allows us to make an important distinction between trivial and nontrivial helping. We show that any wait-free implementation of a queue from Test&Set requires nontrivial helping. We also define a weaker type of nontrivial helping and show that any wait-free queue implementation from a set of arbitrary base objects requires it. In contrast, there is a wait-free implementation of a stack from Test&Set with only trivial helping. These results shed light on the well-known open question of whether there exists a wait-free implementation of a queue in Common2 , and indicate why it seems to be more difficult than implementing a stack. The other approach formalizes the helping mechanism employed by Herlihy's universal wait-free construction and is based on having an operation by one process restrict the possible linearizations of operations by other processes. We show that queue and stack implementations possessing such universal helping can be used to solve consensus. This result can be used to show that a strongly linearizable (Golab et al., 2011) implementation of a queue or a stack for n processes must use objects that allow to solve consensus among n or more processes. Highlights • Two formalizations of helping are presented: nontrivial and universal. • Nontrivial helping separates queues and stacks from Test&Set primitives. • A weaker version of nontrivial helping is introduced and shown necessary in queue implementations. • Universal helping for queues and stacks is universal: it solves consensus. • Strongly linearizable queue or stack for n processes requires primitives with consensus number at least n. [ABSTRACT FROM AUTHOR]

In this paper we recall the construction of two chain level lifts of the gravity operad, one due to Getzler-Kapranov and one due to Westerland. We prove that these two operads are formal and that they indeed have isomorphic homology. [ABSTRACT FROM AUTHOR]

Let (X,D) be a log smooth pair of dimension n, where D is a reduced effective divisor such that the log canonical divisor KX +D is pseudoeffective. Let G be a connected algebraic subgroup of Aut(X, D). We show that G is a semi-abelian variety of dimension = min{n- (V), n} with V := X \D. In the dimension two, Iitaka claimed in his 1979 Osaka J. Math. paper that dimG = q(V) for a log smooth surface pair with (V) = 0 and pg(V) = 1. We (re-)prove and generalize this classical result for all surfaces with = 0 without assuming Iitaka's classification of logarithmic Iitaka surfaces or logarithmic K3 surfaces. [ABSTRACT FROM AUTHOR]

Let X be an Adams geometric stack. We show that D ( A qc ( X ) ) , its derived category of quasi-coherent sheaves, satisfies the axioms of a stable homotopy category defined by Hovey, Palmieri and Strickland in [13] . Moreover we show how this structure relates to the derived category of comodules over a Hopf algebroid that determines X . [ABSTRACT FROM AUTHOR]

For algebraic varieties defined by hyperkähler or, more generally, algebraic symplectic reduction, it is a long-standing question whether the “hyperkähler Kirwan map” on cohomology is surjective. We resolve this question in the affirmative for Nakajima quiver varieties. We also establish similar results for other cohomology theories and for the derived category. Our proofs use only classical topological and geometric arguments. [ABSTRACT FROM AUTHOR]

The weak units of strict monoidal 1- and 2-categories are defined respectively in [15] and [14]. In this paper, we define them for group-like 1- and 2-stacks. We show that they form a contractible Picard 1- and 2-stack, respectively. We give their cohomological description which provides for these stacks a representation by complexes of sheaves of groups. Later, we extend the discussion to the monoidal case. We consider the (2-)substack of cancelable objects of a monoidal 1-(2-)stack. We observe that this (2-)substack is trivially group-like, its weak units are the same as the weak units of the monoidal 1-(2-)stack, and therefore we can recover the contractibility results in [15] and [14] by analysing it. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to lay the foundations of a theory of invariants in étale cohomology for smooth Artin stacks. We compute the invariants in the case of the stack of elliptic curves, and we use the theory we developed to get some results regarding Brauer groups of algebraic spaces. [ABSTRACT FROM AUTHOR]

Vanadium flow battery (VFB) is one of the preferred techniques for efficient large-scale energy storage applications. The key issue for its commercialization is cost reduction, which can be achieved by developing high power density VFB stacks. One of the effective strategies for developing high power density stacks is to enhance the mass transport by performing flow field design. Based on the maldistribution characteristics of concentration polarization inside a conventional rectangular flow battery (RFB), a novel trapezoid flow battery (TFB) was first proposed. Furthermore, a practical and general strategy, consisting of a stepping optimization method and an arithmetic progression model, has been developed for the TFB's structure optimization. By combining numerical simulation with charge-discharge test of the magnified stacks, it was verified that mass transport enhancement and performance improvement of the optimized TFB, with significant increments in voltage efficiency and electrolyte utilization, allowed it to possess great superiority over the RFB. © 2017 American Institute of Chemical Engineers AIChE J, 64: 782-795, 2018 [ABSTRACT FROM AUTHOR]

We prove a structure theorem for relative coarse space morphisms from smooth Deligne- Mumford stacks, showing that each such map can be decomposed in terms of root stack and canonical stack morphisms. We explain how our result can be understood locally in terms of pseudo-reflections. Lastly, we give an application to equivariant K-theory, give several examples illustrating our result, and pose some related questions. [ABSTRACT FROM AUTHOR]

In this paper, we address the Ohmic contacts comparison and optimization on both thin (18 nm) and thick (25 nm) AlGaN/GaN HEMTs structures. In the conventional metallization scheme of Ti/Al/Ti/Au, several stacks based on Ni, Cr, and Pt metals replacing the middle Ti were tested and compared. Specific Contact Resistance (ρ c ) strongly depends on the stack ratio. For a particular, stack ratio of 1:5:2:3 tested on thick AlGaN based HEMTs, Cr stack exhibited the least ρ c value of 5 × 10 −5 Ω-cm 2 while the ρ c value doubled for Pt and increased by 4 times for Ni. But the morphology comparison shows that Ni is the best choice. Therefore the Ni-based stack was further optimized for low contact resistance. In the optimization process, pre-metallization surface treatments were altered along with the stack ratios. The stack ratio of 1:5:2:2.5 has resulted in lowest specific contact resistance value of 6 × 10 −6 Ω-cm 2 . Different Ni-based stacks with ratio variations were then deposited and compared for thick and thin AlGaN/GaN HEMTs structures. The same value of ρ c was recorded on both thick and thin structures as long as the Ni proportion in the stack is low. With an increase in the Ni proportion, ρ c was found to be increased dramatically for thin AlGaN/GaN HEMTs. [ABSTRACT FROM AUTHOR]

We introduce an explicit method for studying actions of a group stack G on an algebraic stack X . As an example, we study in detail the case where X = P ( n 0 , ⋯ , n r ) is a weighted projective stack over an arbitrary base S . To this end, we give an explicit description of the group stack of automorphisms of P ( n 0 , ⋯ , n r ) , the weighted projective general linear 2-group PGL ( n 0 , ⋯ , n r ) . As an application, we use a result of Colliot-Thélène to show that for every linear algebraic group G over an arbitrary base field k (assumed to be reductive if char ( k ) > 0 ) such that Pic ( G ) = 0 , every action of G on P ( n 0 , ⋯ , n r ) lifts to a linear action of G on A r + 1 . [ABSTRACT FROM AUTHOR]

Using Balmer-Favi's generalized idempotents, we establish the telescope conjecture for many algebraic stacks. Along the way, we classify the thick tensor ideals of perfect complexes of stacks. [ABSTRACT FROM AUTHOR]

We prove that the moduli space of stable logarithmic maps with fixed numerical invariants, from logarithmic curves to a fixed projective target logarithmic scheme with fine and saturated logarithmic structure, is a proper algebraic stack. This was previously known only with further restrictions on the logarithmic structure of the target. [ABSTRACT FROM AUTHOR]

We establish several strengthened versions of Lurie's Tannaka duality theorem for certain classes of spectral algebraic stacks. Our most general version of Tannaka duality identifies maps between stacks with exact symmetric monoidal functors between ∞-categories of quasi-coherent complexes which preserve connective and pseudo-coherent complexes. [ABSTRACT FROM AUTHOR]

We prove a general criterion for an algebraic stack to admit a good moduli space. This result may be considered as a generalization of the Keel–Mori theorem, which guarantees the existence of a coarse moduli space for a separated Deligne–Mumford stack. We apply this result to prove that the moduli stacks $\overline{{\mathcal{M}}}_{g,n}(\unicode[STIX]{x1D6FC})$ parameterizing $\unicode[STIX]{x1D6FC}$-stable curves introduced in [J. Alper et al., Second flip in the Hassett–Keel program: a local description, Compositio Math. 153 (2017), 1547–1583] admit good moduli spaces. [ABSTRACT FROM AUTHOR]

We introduce a new moduli stack, called the Serre stable moduli stack, which corresponds to studying families of point objects in an abelian category with a Serre functor. This allows us in particular, to re-interpret the classical derived equivalence between most concealed-canonical algebras and weighted projective lines by showing they are induced by the universal sheaf on the Serre stable moduli stack. We explain why the method works by showing that the Serre stable moduli stack is the tautological moduli problem that allows one to recover certain nice stacks such as weighted projective lines from their moduli of sheaves. As a result, this new stack should be of interest in both representation theory and algebraic geometry. [ABSTRACT FROM AUTHOR]

We propose a categorification of the Chern character that refines earlier work of Toën and Vezzosi and of Ganter and Kapranov. If X is an algebraic stack, our categorified Chern character is a symmetric monoidal functor from a category of mixed noncommutative motives over X , which we introduce, to S 1 -equivariant perfect complexes on the derived free loop stack L X . As an application of the theory, we show that Toën and Vezzosi's secondary Chern character factors through secondary K -theory. Our techniques depend on a careful investigation of the functoriality of traces in symmetric monoidal ( ∞ , n ) -categories, which is of independent interest. [ABSTRACT FROM AUTHOR]

We address the problem of the number of permutations that can be sorted by two stacks in series. We do this by first counting all such permutations of length less than 20 exactly, then using a numerical technique to obtain nineteen further coefficients approximately. Analysing these coefficients by a variety of methods we conclude that the OGF behaves as S ( z ) ∼ A ( 1 − μ ⋅ z ) γ , where μ = 12.45 ± 0.15 , γ = 1.5 ± 0.3 , and A ≈ 0.02 . [ABSTRACT FROM AUTHOR]

The work reported in this paper is focused on the performance of a thermoacoustic refrigerator under various operating conditions. The experiments were conducted with various stack geometries fabricated with epoxy glass and Mylar material. Four stacks with different pore sizes are used to evaluate the performance of the refrigerator. Stack 1 has parallel plates of Mylar material 0.12 mm thick spaced 0.36 mm apart. Stacks 2, 3 and 4 are made of epoxy glass with pores of circular cross-section having 1, 2 and 3 mm diameter, respectively. The entire resonator system was constructed from aluminium material coated with polyurethane material from inside to reduce conduction heat losses. Helium gas was used as a working fluid. The experiments were conducted with different drive ratios ranging from 1.6% to 2% with varying cooling load from 2 to 10 W. For the experiments, operating frequencies from 200 to 600 Hz with mean pressure varying from 2 to 10 bar in steps of 2 bar each were considered. The temperatures of the hot end and cold end of the heat exchangers were recorded using RTDs and a data acquisition system under various operating conditions. The coefficient of performance (COP) and relative COP (COPR) are evaluated. Results show that COP of the refrigerator rises with increase of cooling load and decreases at higher drive ratio. It was also observed that the temperature difference between the hot end and cold end of the stack is higher at 2 W cooling load for 400 Hz operating frequency. The temperature difference between the hot end and cold end of the stack was observed to be 19.4, 17.2, 14 and 12.4°C for stacks 1, 2, 3 and 4, respectively, for 10 bar mean pressure and 2 W cooling load. The temperature difference and COP of the parallel plate stack are better compared with other stack geometries. [ABSTRACT FROM AUTHOR]