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A constructive approach to a conjecture by Voskresenskii
Voskresenskii conjectured that stably rational tori are rational. Klyachko proved this assertion for a wide class of tori by general principles. We...
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On abstract representations of the groups of rational points of algebraic groups in positive characteristic
We analyze the structure of a large class of connected algebraic rings over an algebraically closed field of positive characteristic using...
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Good reduction of algebraic groups and flag varieties
In 1983, Faltings proved that there are only finitely many abelian varieties over a number field of fixed dimension and with good reduction outside a...
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Which algebraic groups are Picard varieties?
We show that every connected commutative algebraic group over an algebraically closed field of characteristic 0 is the Picard variety of some...
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On the “Galois Closure” for Finite Morphisms
We give necessary and sufficient conditions for a finite flat morphism of schemes of characteristic Hurwitz stacks.p > 0 to be dominated by a torsor...
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Fundamental Groupoid Scheme
This article is an overview of the original construction by Nori of the fundamental group scheme as the Galois group of some Tannaka category EF(X)...
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The Coherent Cohomology Ring of an Algebraic Group
Let G be a group scheme of finite type over a field, and consider the cohomology ring H * ( G ) with coefficients in the structure sheaf. We show that H ...
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Vector bundles over normal varieties trivialized by finite morphisms
Let Y be a normal and projective variety over an algebraically closed field k and V a vector bundle over Y . We prove that if there exist a k -scheme X ...
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Extension of finite solvable torsors over a curve
Let R be a complete discrete valuation ring with fraction field K and with algebraically closed residue field of positive characteristic p . Let X be...
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On the Geometry of Global Function Fields, the Riemann–Roch Theorem, and Finiteness Properties of S-Arithmetic Groups
In this survey I sketch Behr–Harder reduction theory for reductive groups over global functions fields and briefly describe its applicability in the...
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Remarks on the Isotriviality of Multiloop Algebras
For a given finite dimensional simple Lie algebra g over an algebraically closed field of characteristic 0, we establish the existence of a positive...
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Factorisation properties of group scheme actions
Let H be an algebraic group scheme over a field k acting on a commutative k -algebra A which is a unique factorisation domain. We show that, under...
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Differential operators and automorphism schemes
The ring of global differential operators of a variety is in closed and deep relation with its automorphism scheme. This relation can be applied to...
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Gersten conjecture for equivariant K-theory and applications
For a reductive group scheme G over a regular semi-local ring A , we prove the Gersten conjecture for the equivariant K -theory. As a consequence, we...
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Foliations in Moduli Spaces of Abelian Varieties and Dimension of Leaves
In moduli spaces of abelian varieties and of p-divisible groups in characteristic p we have various foliations and statifications. In this paper we...
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Reduction of structure for torsors over semilocal rings
Let G be a reductive affine group scheme defined over a semilocal ring k . Assume that either G is semisimple or k is normal and noetherian. We show...
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On Weil restriction of reductive groups and a theorem of Prasad
Let G be a connected simple semisimple algebraic group over a local field F of arbitrary characteristic. In a previous article by the author the...