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We show that Bloch's complex of relative zero-cycles can be used as a dualizing complex over perfect fields and number rings. This leads to duality theorems for torsion sheaves on arbitrary separated schemes of finite type over…

Algebra and representation theory in modular tensor categories can be combined with tools from topological field theory to obtain a deeper understanding of rational conformal field theories in two dimensions: It allows us to establish the…

In this short note we prove a version of Bertini's theorem for unipotent rigid fundamental groups, stating that for every smooth, projective, geometrically connected variety $X$ over an infinite perfect field $k$ of characteristic $p>0$,…

Let $X$ denote an equivariant embedding of a connected reductive group $G$ over an algebraically closed field $k$. Let $B$ denote a Borel subgroup of $G$ and let $Z$ denote a $B \times B$-orbit closure in $X$. When the characteristic of $k$…

We consider parahoric Bruhat-Tits group schemes over a smooth projective curve and torsors under them. If the characteristic of the ground field is either zero or positive but not too small and the generic fiber is absolutely simple and…

Let $U$ be a smooth and connected curve over an algebraically closed field of positive characteristic, with smooth compactification $X$. We generalize classical Geometric Class Field theory to provide a classification of fppf $G$-torsors…

We prove that every finite symmetric integral tensor category $\mathcal{C}$ with the Chevalley property over an algebraically closed field $k$ of characteristic $p>2$ admits a symmetric fiber functor to $\text{sVec}$. This proves Ostrik's…

We prove a rigidity theorem for the Poisson automorphisms of the function fields of tori with quadratic Poisson structures over fields of characteristic 0. It gives an effective method for classifying the full Poisson automorphism groups of…

Let X be a smooth double cover of a geometrically ruled surface defined over a separably closed field of characteristic different from 2. The main result of this paper is a finite presentation of the 2-torsion in the Brauer group of X with…

Let $X$ be a cubic fourfold in $P^5_{C}$. We prove that, assuming the Hodge conjecture for the product $S \times S$, where $S$ is a complex surface, and the finite dimensionality of the Chow motive $h(S)$, there are at most a countable…

Consider a connected topological space $X$ with a point $x \in X$ and let $K$ be a field with the discrete topology. We study the Tannakian category of finite dimensional (flat) vector bundles on $X$ and its Tannakian dual $\pi_K (X,x)$…

Let k be a number field and X a smooth projective k-variety. In this paper, we study the information obtainable from descent via torsors under finite k-group schemes on the location of the k-rational points on X within the adelic points.…

In this note we extend some of the results of a previous paper \url{arXiv:math/0511593} to algebraically closed fields of finite characteristic. In particular, we show that there is an explicit expression in $n$ and $d$ which is divisible…

This work concerns the stable module category of a finite group over a field of characteristic dividing the group order. The minimal localising tensor ideals correspond to the non-maximal homogeneous prime ideals in the cohomology ring of…

Let $G$ be a finite group and $k$ a field of prime characteristic $p$. We give a complete classification of endotrivial complexes, i.e. determine the Picard group $\mathcal{E}_k(G)$ of the tensor-triangulated category…

Esnault-Viehweg developed the theory of cyclic branched coverings $\tilde X\to X$ of smooth surfaces providing a very explicit formula for the decomposition of $H^1(\tilde X,\mathbb{C})$ in terms of a resolution of the ramification locus.…

We show that the subgroup of the Picard group of a $p$-block of a finite group given by bimodules with endopermutation sources modulo the automorphism group of a source algebra is determined locally in terms of the fusion system on a defect…

Let $\mathcal{V}$ be a mixed characteristic complete discrete valuation ring, $\mathcal{P}$ a separated smooth formal scheme over $\mathcal{V}$, $P$ its special fiber, $X$ a smooth closed subscheme of $P$, $T$ a divisor in $P$ such that…

This thesis is devoted to the study of abelian automorphism groups of surfaces and $3$-folds of general type over complex number field $\Bbb C$. We obtain a linear bound in $K^3$ for abelian automorphism groups of $3$-folds of general type…

For the cyclic group $C_2$ we give a complete description of the derived category of perfect complexes of modules over the constant Mackey ring $\underline{\mathbb{Z}/\ell}$, for $\ell$ a prime. This is fairly simple for $\ell$ odd, but for…