de Rham Theory for Tame Stacks and Schemes with Linearly Reductive Singularities

Matthew Satriano[1]

  • [1] University of Michigan Department of Mathematics 2074 East Hall, Ann Arbor, MI 48109-1043 (USA)

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 6, page 2013-2051
  • ISSN: 0373-0956

Abstract

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We prove that the Hodge-de Rham spectral sequence for smooth proper tame Artin stacks in characteristic p (as defined by Abramovich, Olsson, and Vistoli) which lift mod p 2 degenerates. We push the result to the coarse spaces of such stacks, thereby obtaining a degeneracy result for schemes which are étale locally the quotient of a smooth scheme by a finite linearly reductive group scheme.

How to cite

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Satriano, Matthew. "de Rham Theory for Tame Stacks and Schemes with Linearly Reductive Singularities." Annales de l’institut Fourier 62.6 (2012): 2013-2051. <http://eudml.org/doc/251087>.

@article{Satriano2012,
abstract = {We prove that the Hodge-de Rham spectral sequence for smooth proper tame Artin stacks in characteristic $p$ (as defined by Abramovich, Olsson, and Vistoli) which lift mod $p^2$ degenerates. We push the result to the coarse spaces of such stacks, thereby obtaining a degeneracy result for schemes which are étale locally the quotient of a smooth scheme by a finite linearly reductive group scheme.},
affiliation = {University of Michigan Department of Mathematics 2074 East Hall, Ann Arbor, MI 48109-1043 (USA)},
author = {Satriano, Matthew},
journal = {Annales de l’institut Fourier},
keywords = {de Rham; Hodge; tame stack; linearly reductive},
language = {eng},
number = {6},
pages = {2013-2051},
publisher = {Association des Annales de l’institut Fourier},
title = {de Rham Theory for Tame Stacks and Schemes with Linearly Reductive Singularities},
url = {http://eudml.org/doc/251087},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Satriano, Matthew
TI - de Rham Theory for Tame Stacks and Schemes with Linearly Reductive Singularities
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 6
SP - 2013
EP - 2051
AB - We prove that the Hodge-de Rham spectral sequence for smooth proper tame Artin stacks in characteristic $p$ (as defined by Abramovich, Olsson, and Vistoli) which lift mod $p^2$ degenerates. We push the result to the coarse spaces of such stacks, thereby obtaining a degeneracy result for schemes which are étale locally the quotient of a smooth scheme by a finite linearly reductive group scheme.
LA - eng
KW - de Rham; Hodge; tame stack; linearly reductive
UR - http://eudml.org/doc/251087
ER -

References

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  15. Martin C. Olsson, Hom ̲ -stacks and restriction of scalars, Duke Math. J. 134 (2006), 139-164 Zbl1114.14002MR2239345
  16. Martin C. Olsson, Sheaves on Artin stacks, J. Reine Angew. Math. 603 (2007), 55-112 Zbl1137.14004MR2312554
  17. Matthew Satriano, A generalization of the Chevalley-Shephard-Todd theorem to the case of linearly reductive group schemes, (2009) Zbl1252.14002
  18. J. H. M. Steenbrink, Mixed Hodge structure on the vanishing cohomology, Real and complex singularities (Proc. Ninth Nordic Summer School/NAVF Sympos. Math., Oslo, 1976) (1977), 525-563, Sijthoff and Noordhoff, Alphen aan den Rijn Zbl0373.14007MR485870
  19. B. Toen, K-théorie et cohomologie des champs algébriques: Théorèmes de Riemann-Roch, D-modules et théorèmes GAGA, (1999) 
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