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We study Néron models of pseudo-Abelian varieties over excellent discrete valuation rings of equal characteristic p > 0 and generalise the notions of good reduction and semi- Abelian reduction to such algebraic groups. We prove that the well-known representationtheoretic criteria for good and semi-Abelian reduction due to Néron--Ogg--Shafarevich and Grothendieck carry over to the pseudo-Abelian case, and give examples to show that our results are the best possible in most cases. Finally, we study the order of the group scheme of connected components of the Néron model in the pseudo-Abelian case. Our method is able to control the Ι-part (for Ι ≠ p) of this order completely, and we study the p-part in a particular (but still reasonably general) situation. [ABSTRACT FROM AUTHOR]

Let $X$ be a smooth geometrically connected projective curve over the field of fractions of a discrete valuation ring $R$ , and $\mathfrak {m}$ a modulus on $X$ , given by a closed subscheme of $X$ which is geometrically reduced. The generalized Jacobian $J_\mathfrak {m}$ of $X$ with respect to $\mathfrak {m}$ is then an extension of the Jacobian of $X$ by a torus. We describe its Néron model, together with the character and component groups of the special fibre, in terms of a regular model of $X$ over $R$. This generalizes Raynaud's well-known description for the usual Jacobian. We also give some computations for generalized Jacobians of modular curves $X_0(N)$ with moduli supported on the cusps. [ABSTRACT FROM AUTHOR]

Let Z be a nondegenerate hypersurface in a d-dimensional torus (C*)d defined by a Laurent polynomial f with a d-dimensional Newton polytope P. The subset F(P) ⊂ P consisting of all points in P having integral distance at least 1 to all integral supporting hyperplanes of P is called the Fine interior of P. If F(P) ≠ ∅, we construct a unique projective model Z of Z having at worst canonical singularities and obtain minimal models Z of Z by crepant morphisms b Z → Z. We show that the Kodaira dimension κ = κ(Z) equals min{d - 1, dim F(P)} and the general fibers in the Iitaka fibration of the canonical model Z are nondegenerate (d - 1 - ΰ)-dimensional toric hypersurfaces of Kodaira dimension 0. Using F(P), we obtain a simple combinatorial formula for the intersection number (KZ)d-1. [ABSTRACT FROM AUTHOR]

Minimal Model (MM) is the top-scoring model for assessing physiological characteristics to diagnose the potential or onset of type 2 diabetes mellitus (T2DM) through the intravenous glucose tolerance test (IVGTT) for the past four decades. Nevertheless it has been arguable that MM method either overestimates glucose effectiveness (GE) or underestimates insulin sensitivity (IS) in some cases by both biologists through in vivo experiments and mathematicians by analysis and/or simulations. We propose a novel model including the interstitial insulin according to physiology and adapted from the well accepted Sturis' model for the glucose-insulin metabolic system suitable to the IVGTT setting. Our model consistently overcomes the aforementioned defects in a subgroup of subjects. In addition, the variable X for insulin action in MM might be appropriately interpreted as an increment of insulin in the interstitial space in response to the bolus stimulus, rather than being proportional to the interstitial insulin as believed. [ABSTRACT FROM AUTHOR]

We work with a smooth relative curve XU/U with nodal reduction over an excellent and locally factorial scheme S. We show that blowing up a nodal model of XU in the ideal sheaf of a section yields a new nodal model and describe how these models relate to each other. We construct a Néron model for the Jacobian of XU and describe it locally on S as a quotient of the Picard space of a well-chosen nodal model. We provide a combinatorial criterion for the Néron model to be separated. [ABSTRACT FROM AUTHOR]