Nonabelian Hodge theory in characteristic p

A. Ogus; V. Vologodsky

Publications Mathématiques de l'IHÉS (2007)

  • Volume: 106, page 1-138
  • ISSN: 0073-8301

Abstract

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Given a scheme in characteristic p together with a lifting modulo p2, we construct a functor from a category of suitably nilpotent modules with connection to the category of Higgs modules. We use this functor to generalize the decomposition theorem of Deligne-Illusie to the case of de Rham cohomology with coefficients.

How to cite

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Ogus, A., and Vologodsky, V.. "Nonabelian Hodge theory in characteristic $p$." Publications Mathématiques de l'IHÉS 106 (2007): 1-138. <http://eudml.org/doc/104228>.

@article{Ogus2007,
abstract = {Given a scheme in characteristic p together with a lifting modulo p2, we construct a functor from a category of suitably nilpotent modules with connection to the category of Higgs modules. We use this functor to generalize the decomposition theorem of Deligne-Illusie to the case of de Rham cohomology with coefficients.},
author = {Ogus, A., Vologodsky, V.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {Hodge theory; non-Abelian theory; Higgs bundles; Higgs field; de Rham cohomology; Higgs cohomology; Riemann-Hilbert correspondence; Azumaya algebras},
language = {eng},
pages = {1-138},
publisher = {Springer},
title = {Nonabelian Hodge theory in characteristic $p$},
url = {http://eudml.org/doc/104228},
volume = {106},
year = {2007},
}

TY - JOUR
AU - Ogus, A.
AU - Vologodsky, V.
TI - Nonabelian Hodge theory in characteristic $p$
JO - Publications Mathématiques de l'IHÉS
PY - 2007
PB - Springer
VL - 106
SP - 1
EP - 138
AB - Given a scheme in characteristic p together with a lifting modulo p2, we construct a functor from a category of suitably nilpotent modules with connection to the category of Higgs modules. We use this functor to generalize the decomposition theorem of Deligne-Illusie to the case of de Rham cohomology with coefficients.
LA - eng
KW - Hodge theory; non-Abelian theory; Higgs bundles; Higgs field; de Rham cohomology; Higgs cohomology; Riemann-Hilbert correspondence; Azumaya algebras
UR - http://eudml.org/doc/104228
ER -

References

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