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Background Paediatric Cryptococcus gattii disease is rare, with only two previous cases recorded in the Northern Territory (NT) over the last 54 years. Immune reconstitution inflammatory syndrome (IRIS) is a recognised complication of C. gattii infection, even in the absence of an identified immunodeficiency syndrome; however, limited paediatric data exist. We present a series of three paediatric patients treated for C. gattii infection in the NT during 2016/2017. Case discussions All three cases were males aged 8-13 years at the time of presentation. Two were Aboriginal Australians from remote NT communities, and the third was a Timorese child from a remote district in Timor-Leste. All cases had evidence of brain cryptococcomas, and two had associated pulmonary lesions. Each child was treated with a 6-week induction phase of intravenous liposomal amphotericin and flucytosine and then continued on a 2-year course of eradication oral fluconazole. Persistent high intracranial pressure (ICP) complicated each case, requiring serial lumbar punctures and, in two cases, insertion of ventriculoperitoneal shunts. All three cases were diagnosed with IRIS between 5 and 10 weeks after commencement of antifungal treatment and were managed with high-dose corticosteroids, which were weaned slowly (6-20 months post-commencement). Conclusions Paediatric C. gattii disease is rare, although three recent cases in the NT highlight some of the challenges involved in managing the infection, including persistent raised ICP and complications such as IRIS. There is a need for further collaborative research into paediatric C. gattii disease.

AIM To describe the epidemiology of invasive Salmonella disease in children in the Northern Territory, Australia. METHODS Design: A retrospective review of invasive salmonellosis cases identified by pathology records and the Northern Territory Notifiable Disease Surveillance System. Case definitions: Those aged 18 years or under, with Salmonella cultured from a usually sterile site, collected in the Northern Territory between 1 July 2005 and 30 June 2015. OUTCOME MEASURES The primary outcome measure was the annual incidence rate of invasive salmonellosis, comparing rates between Indigenous and non-Indigenous children. RESULTS There were 86 cases of invasive Salmonella infection in children over the 10-year period; an annual incidence of 14.1 per 100 000 population, in those aged less than 18 years. Gastrointestinal Salmonella notifications were similar between Indigenous and non-Indigenous children. In children aged less than 15 years, the rate of invasive salmonellosis was higher in Indigenous children compared to non-Indigenous children (23.4 per 100 000 compared with 11.6 per 100 000); rate ratio 2.0 (95% confidence interval 1.3-3.3, P = 0.002). Indigenous children with invasive salmonellosis had a median hospital stay of 8 days, which was compared to 5 days for non-Indigenous children (P = 0.015). The highest incidence rate of invasive salmonellosis occurred in Indigenous patients less than 12 months of age (138 per 100 000). CONCLUSION The Northern Territory of Australia has high rates of invasive salmonellosis in children. Indigenous and non-Indigenous children experience similar rates of Salmonella gastroenteritis but Indigenous children experience higher rates of invasive salmonellosis.

Our team was referred a 14-year-old, previously healthy, immunised aboriginal boy from a remote community in northern Western Australia. He had been admitted to the local community hospital 10 days previously and while there developed haemoptysis, fever and epigastric abdominal pain so was transferred to our care at the regional hospital for ongoing investigation and management. Haemoptysis is an uncommon presentation in adolescence. It can be caused by infection (eg, bronchiectasis, pneumonia, lung abscess or tuberculosis), trauma (eg, lung contusion, foreign body or inhalation injury), vascular disorders (eg, pulmonary embolus, arteriovenous malformation or haemangioma), late complications of congenital lung malformations, coagulopathy or one of the diffuse alveolar haemorrhage syndromes.1 Additionally, bleeding from the upper airway or gastrointestinal tract can mimic haemoptysis. Demographic considerations are important in this case. Bronchiectasis and rheumatic heart disease, both of which may present with haemoptysis, have increased prevalence in aboriginal children in Australia. In addition, Burkholderia pseudomallei is endemic and pulmonary infection can mimic tuberculosis. An infectious aetiology is favoured here in view of the history of fever. He had initially been admitted to the local hospital with presumed bacterial meningitis following presentation with headache, fever and meningism 10 days prior. Cerebrospinal fluid (CSF) prior to antibiotics demonstrated elevated white cell count (WCC) 550/mm3 (90% neutrophils) and protein (0.84 g/L), with negative microscopy and culture for bacteria, and negative PCR testing for bacteria and viruses. Intravenous ceftriaxone (ongoing) and dexamethasone 0.15 mg/kg four times a day (total 4 days) had been administered, with rapid resolution of symptoms. Following transfer to our care (day 1), examination showed normal respiratory rate and oxygen saturations (SaO2=98%); a productive cough with a moderate amount of blood-stained sputum was noted. The respiratory examination (including upper airway) was otherwise unremarkable. There was mild right upper quadrant abdominal tenderness …

Nontuberculous mycobacteria (NTM) are ubiquitous organisms in our surrounding environment. Four distinct clinical syndromes associated with NTM infection have been described: skin and soft tissue disease, lymphadenitis, disseminated disease and pulmonary disease. In children, lymphadenitis is the most common NTM clinical entity, particularly affecting those aged 1-5 years who have no known risk factors for disease. Optimal management of NTM lymphadenitis is not entirely clear, although surgical intervention is likely a definitive therapy. Disseminated NTM disease is uncommon and only seen in the setting of immunocompromise. In previously well children, this presentation should always lead to consideration of an underlying immune defect, such as Mendelian susceptibility to mycobacterial disease. Identification of the underlying cause enables more targeted therapy and better prognostic understanding. Pulmonary NTM disease is fundamentally different to the other clinical syndromes, presenting in different hosts, who have different comorbidities, and follow a different clinical course.

Let T/A be an integral extension of noetherian integrally closed integral domains whose quotient field extension is a finite cyclic Galois extension. Let S/R be a localization of this extension which is unramified. Using a generalized cyclic crossed product construction it is shown that certain reflexive fractional ideals of T with trivial norm give rise to Azumaya R-algebras that are split by S. Sufficient conditions on T/A are derived under which this construction can be reversed and the relative Brauer group of S/R is shown to fit into the exact sequence of Galois cohomology associated to the ramified covering T/A. Many examples of affine algebraic varieties are exhibited for which all of the computations are carried out.

We study algebras and divisors on a normal affine hypersurface defined by an equation of the form z n = f ( x 1 , … , x m ) . The coordinate ring is T = k [ x 1 , … , x m , z ] / ( z n − f ) , and if R = k [ x 1 , … , x m ] [ f − 1 ] and S = R [ z ] / ( z n − f ) , then S is a cyclic Galois extension of R . We show that if the Galois group is G , the natural map H 1 ( G , Cl ( T ) ) → H 1 ( G , Pic ( S ) ) factors through the relative Brauer group B ( S / R ) and that all of the maps are onto. Sufficient conditions are given for H 1 ( G , Cl ( T ) ) to be isomorphic to B ( S / R ) . As an example, all of the groups, maps, divisors and algebras are computed for an affine surface defined by an equation of the form z n = ( y − a 1 x ) ⋯ ( y − a n x ) ( x − 1 ) .

Elementary examples are presented of normal algebraic surfaces X with singular points x such that at the local ring 𝒪 X, x there exist Azumaya algebras of all orders in the Brauer group that are split by the field of rational functions on X. These algebra classes correspond to elements of torsion in the class group of the henselian local ring . The surfaces X are affine normal rational and the singularities x are nonrational.

We study algebra classes and divisor classes on a normal affine surface of the form z 2 = f(x, y). The affine coordinate ring is T = k[x, y, z]/(z 2 − f), and if R = k[x, y][f −1] and S = R[z]/(z 2 − f), then S is a quadratic Galois extension of R. If the Galois group is G, we show that the natural map H1(G, Cl(T)) → H1(G, Pic(S)) factors through the relative Brauer group B(S/R) and that all of the maps are onto. Sufficient conditions are given for H1(G, Cl(T)) to be isomorphic to B(S/R). The groups and maps are computed for several examples.

The object of study is the family of normal affine algebraic surfaces defined by equations of the form z n = ( y − a 1 x ) ⋯ ( y − a n x ) ( x − 1 ) . Each surface X in this family is rational and contains a non-rational singularity. Using an explicit resolution of the singularity, many computations involving Weil divisors and Azumaya algebras on X are completely carried out. The Picard group and Brauer group are shown to depend in subtle ways on the values a 1 , … , a n . For an odd prime n, and for a general choice of X, the Picard group and the Brauer group are computed.

We study the finite-dimensional central division algebras over the rational function field in several variables over an algebraically closed field. We describe the division algebras that are split by the cyclic covering obtained by adjoining the n th root of a polynomial. The relative Brauer group is described in terms of the Picard group of the cyclic covering and its Galois group. Many examples are given and in most cases division algebras are presented that represent generators of the relative Brauer group.

Let be a complete fan in such that every three-dimensional cone in is non-simplicial. In any non-empty open neighborhood of there is a fan such that every -linear support function is linear and the Picard group of the associated toric variety is zero.

Associated to a finite distributive lattice L is a projective variety V ( L ). It is shown that the cohomological Brauer group of V ( L ) is trivial.

Let V be a reduced projective hypersurface in P v and C the affine cone over V in X = A v + 1 . We employ cohomological methods to study the Brauer groups of the varieties C , C - P , X - C and X ¯ - C ¯ , where P is the vertex of the cone, X ¯ = P v + 1 and C is the completion of C in X .

The object of study is the group of units 𝒪*(X) in the coordinate ring of a normal affine variety X over an algebraically closed field k. Methods of Galois cohomology are applied to those varieties that can be presented as a finite cyclic cover of a rational variety. On a cyclic cover X → 𝔸m of affine m-space over k such that the ramification divisor is irreducible and the degree is prime, it is shown that 𝒪*(X) is equal to k*, the non-zero scalars. The same conclusion holds, if X is a sufficiently general affine hyperelliptic curve. If X has a projective completion such that the divisor at infinity has r components, then sufficient conditions are given for 𝒪*(X)/k* to be isomorphic to ℤ(r-1).

For an affine double plane defined by an equation of the form z^2 = f, we study the divisor class group and the Brauer group. Two cases are considered. In the first case, f is a product of n linear forms in k[x,y] and X is birational to a ruled surface P^1 x C, where C is rational if n is odd and hyperelliptic if n is even. In the second case, f is the equation of an affine hyperelliptic curve. On the open set where the cover is unramified, we compute the groups of divisor classes, the Brauer groups, the relative Brauer group, as well as all of the terms in he exact sequence of Chase, Harrison and Rosenberg.

LetK be the field of fractions of a curve overR whereR is the henselization of a regular local ring on an algebraic curve over a field which is algebraically closed and has characteristic 0. ThenK has the exponent=degree property for division algebras. In fact every central finite dimensionalK-division algebra with exponentn is a cyclic algebra of degreen.

If K is an algebraically closed field, then it is known that K [ y ] has the coefficient assignment property. Conversely, suppose that the field K has characteristic zero and contains the primitive n th roots of unity for all positive integers n . If K [ y ] has the coefficient assignment property, then K is closed under taking n th roots for all positive integers n .

Associated to a toric variety $X$ of dimension $r$ over a field $k$ is a fan $\Delta$ on $\Bbb R^r$. The fan $\Delta$ is a finite set of cones which are in one-to-one correspondence with the orbits of the torus action on $X$. The fan $\Delta$ inherits the Zariski topology from $X$. In this article some cohomological invariants of $X$ are studied in terms of whether or not they depend only on $\Delta$ and not $k$. Secondly some numerical invariants of $X$ are studied in terms of whether or not they are topological invariants of the fan $\Delta$. That is, whether or not they depend only on the finite topological space defined on $\Delta$. The invariants with which we are mostly concerned are the class group of Weil divisors, the Picard group, the Brauer group and the dimensions of the torsion free part of the \'etale cohomology groups with coefficients in the sheaf of units. The notion of an open neighborhood of a fan is introduced and examples are given for which the above invariants are sufficiently fine to give nontrivial stratifications of an open neighborhood of a fan all of whose maximal cones are nonsimplicial., Comment: 16 pages with 2 figures, Author-supplied DVI file available at ftp://ftp.math.fau.edu/pub/Ford/itv.dvi, Author-supplied PostScript file available at ftp://ftp.math.fau.edu/pub/Ford/itv.ps, AMSLaTeX v 1.2

We compute the cohomological Brauer group of a normal toric variety whose singular locus has codimension less than or equal to 2 everywhere

Let X be a smooth variety over an algebraically closed field k and Y a closed subvariety of codimension 1. We associate to Y a graph Γ and use the homology of Γ to study the Brauer group of X — Y.

Let Z be a nonsingular plane curve of even degree and U = P 2 — Z. Let : X —> P 2 be tbe double cover ramified over Z and V = —1(U). It is shown that the kernel of the restriction map on Brauer groups" : B(U) —> B(V), is isomorphic to Z/2(2) where ρ— 2 Pic X is an isomorphism, exactly half of the algebra classes of order 2 in B(X) are restrictions of algebra classes of order 2 in B(U) whose ramification has been split by V. The kernel of the corestriction map 2 B(V) — 2B(U) is shown to be the subgroup consisting of elements fixed by the Galois group.

A covariant functor has been defined in [1] which assigns to a commutative ring R an abelian monoid m(R). The elements of m(R) are equivalence classes (called homotopy classes) of homomorphisms of progenerator modules over R. The monoid homomorphism m(σ): m(R) → m(S) associated with a homomor-phism of rings σ: R → S is studied. Both necessary condi­tions and sufficient conditions for m(σ)1 {1} = {1}, for m(σ) to be injective and for m(σ) to be surjective are presented.

The Brauer-Long group of Z/2 dimodule algebras over a connected commutative ring R in which 2 is invertible is computed in terms of the cohomology of R. Consequences of this calculation are given.

Let R be a commutative noetherian ring. We compute the n -torsion part of the Brauer group of R [ t , 1/ t ] for each positive integer n such that n is relatively prime to all of the residue characteristics of R .

Homomorphisms defined on progenerator modules over a commutative ring are studied through the introduction of a relation called homotopy, which is coarser than the usual notion of equivalence. The set of homotopy classes of homomorphisms forms a commutative monoid with operation induced by tensor product. For a given commutative ring, classification of homomorphisms is carried out by determining the algebraic structure of the monoid of homotopy classes and then giving a representing homomorphism for each class. This classification is carried out explicitly for Dedekind domains.

A central division algebra over the field of rational functions in two variables with coefficients over an algebraically closed field ramifies along a divisor on the projective plane. If the ramification divisor is a quartic curve which is the union of a nodal cubic and a line, we show that the division algebra is a symbol algebra and satisfies the “index equals exponent” equation.

This article is concerned with the cup product map μ:H1 (X, Z/n)⊗H1 (X, Z/n) → nB(X). Under certain conditions we describe the image and kernel of μ for the spectrum of k[s1, …, x v , f−1] and for a fiber product space.