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Title of Journal: manuscripta math

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Abbravation: manuscripta mathematica

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Springer-Verlag

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DOI

10.1002/chin.201608031

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1432-1785

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Reduction of structure for torsors over semilocal

Authors: V Chernousov P Gille Z Reichstein
Publish Date: 2008/03/26
Volume: 126, Issue: 4, Pages: 465-480
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Abstract

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 that G has a finite ksubgroup S such that the natural map H 1R S → H 1R G is surjective for every semilocal ring R containing k In other words Gtorsors over SpecR admit reduction of structure to S We also show that the natural map H 1X S → H 1X G is surjective in several other contexts under suitable assumptions on the base ring k the scheme X/k and the group scheme G/k These results have already been used to study loop algebras and essential dimension of connected algebraic groups in prime characteristic Additional applications are presented at the end of this paper

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  1. A stability criterion for nonparametric minimal submanifolds
  2. Harmonic maps and asymptotic Teichmüller space
  3. On the backward uniqueness property for the heat equation in two-dimensional conical domains
  4. Minoration de la hauteur de Néron-Tate sur les surfaces abéliennes
  5. Stability of flows associated to gradient vector fields and convergence of iterated transport maps
  6. Willmore submanifolds of the Möbius space and a Bernstein-type theorem
  7. A positivity property of the Satake isomorphism
  8. Homological characterization of lean algebras
  9. Common divisors of elliptic divisibility sequences over function fields
  10. Finitistic dimensions of semiprimary rings
  11. Extending Elliptic Curve Chabauty to higher genus curves
  12. The Sp 3 -grassmannian and duality for prime Fano threefolds of genus 9
  13. Existence and compactness for the $${\overline{\partial}}$$ -Neumann operator on q-convex domains
  14. The normalization constant of a certain invariant measure on GL n ()
  15. Tropical descendant Gromov–Witten invariants
  16. A Harnack inequality for the quasi-minima of scalar integral functionals with general growth conditions
  17. Cut loci and conjugate loci on Liouville surfaces
  18. A sphere theorem on locally conformally flat even-dimensional manifolds
  19. On the class numbers of certain Hilbert class fields
  20. The zeros of certain weakly holomorphic Drinfeld modular forms
  21. Icosahedral representations and elliptic curves
  22. On entire functions whose derivatives are¶integer-valued on geometric progressions
  23. Perversité et variation
  24. On linear combinations of special values of L -functions
  25. Irrationalité de certaines sommes de séries
  26. Deformations of Koszul Artin–Schelter Gorenstein algebras
  27. On positive definite hermitian forms
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