Nonabelian Hodge theory in characteristic p
By A. Ogus, V. Vologodsky. 2005
163 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/de6bb0593a539b7dfd12050fa1ec5905a07ca8b3
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Hodge theoretic aspects of mirror symmetry (2008, background): “The latter satisfies the degeneration property by the work of Barannikov and the second author, Sabbah [Sab99], or Ogus-Vologodsky [OV05].”
- Bogomolov’s inequality for Higgs sheaves in positive characteristic (2015, background): “2.3 Simpson’s correspondence in positive characteristic In this subsection we recall the main results of Ogus and Vologodsky [31].”
- Holonomic -modules and positive characteristic (2009, unknown): “It follows directly from definitions that the arithmetic support of M (at prime p) is the same as the support of Higgs (compare with [12]).”
- Semistable Higgs bundles, periodic Higgs bundles and representations of algebraic fundamental groups (2013, methodology): “In [25], they construct the inverse Cartier transform from the category of (suitably nilpotent) Higgs modules over X ′ 1 = X1 ×Fk Spec k to the category of (suitably nilpotent) flat modules over X1.”
- Singular Localization and Intertwining Functors for Reductive Lie Algebras in Prime Characteristic (2006, background): “6An Azumaya algebra is a sheaf of locally matrix algebras in etale topology [Mln]. 7See also [ OV ] for more information.”