Tame stacks in positive characteristic

Dan Abramovich[1]; Martin Olsson[2]; Angelo Vistoli[3]

  • [1] Brown University Department of Mathematics Box 1917 Providence, RI 02912 (USA)
  • [2] University of California Department of Mathematics #3840 Berkeley, CA 94720-3840 (USA)
  • [3] Scuola Normale Superiore Piazza dei Cavalieri 7 56126 Pisa (Italy)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 4, page 1057-1091
  • ISSN: 0373-0956

Abstract

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We introduce and study a class of algebraic stacks with finite inertia in positive and mixed characteristic, which we call tame algebraic stacks. They include tame Deligne-Mumford stacks, and are arguably better behaved than general Deligne-Mumford stacks. We also give a complete characterization of finite flat linearly reductive schemes over an arbitrary base. Our main result is that tame algebraic stacks are étale locally quotient by actions of linearly reductive finite group schemes.

How to cite

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Abramovich, Dan, Olsson, Martin, and Vistoli, Angelo. "Tame stacks in positive characteristic." Annales de l’institut Fourier 58.4 (2008): 1057-1091. <http://eudml.org/doc/10342>.

@article{Abramovich2008,
abstract = {We introduce and study a class of algebraic stacks with finite inertia in positive and mixed characteristic, which we call tame algebraic stacks. They include tame Deligne-Mumford stacks, and are arguably better behaved than general Deligne-Mumford stacks. We also give a complete characterization of finite flat linearly reductive schemes over an arbitrary base. Our main result is that tame algebraic stacks are étale locally quotient by actions of linearly reductive finite group schemes.},
affiliation = {Brown University Department of Mathematics Box 1917 Providence, RI 02912 (USA); University of California Department of Mathematics #3840 Berkeley, CA 94720-3840 (USA); Scuola Normale Superiore Piazza dei Cavalieri 7 56126 Pisa (Italy)},
author = {Abramovich, Dan, Olsson, Martin, Vistoli, Angelo},
journal = {Annales de l’institut Fourier},
keywords = {Algebraic stacks; moduli spaces; group schemes; algebraic stacks},
language = {eng},
number = {4},
pages = {1057-1091},
publisher = {Association des Annales de l’institut Fourier},
title = {Tame stacks in positive characteristic},
url = {http://eudml.org/doc/10342},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Abramovich, Dan
AU - Olsson, Martin
AU - Vistoli, Angelo
TI - Tame stacks in positive characteristic
JO - Annales de l’institut Fourier
PY - 2008
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 4
SP - 1057
EP - 1091
AB - We introduce and study a class of algebraic stacks with finite inertia in positive and mixed characteristic, which we call tame algebraic stacks. They include tame Deligne-Mumford stacks, and are arguably better behaved than general Deligne-Mumford stacks. We also give a complete characterization of finite flat linearly reductive schemes over an arbitrary base. Our main result is that tame algebraic stacks are étale locally quotient by actions of linearly reductive finite group schemes.
LA - eng
KW - Algebraic stacks; moduli spaces; group schemes; algebraic stacks
UR - http://eudml.org/doc/10342
ER -

References

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