Search results for "14F30"

showing 2 items of 2 documents

A note on the characteristic $p$ nonabelian Hodge theory in the geometric case

2012

We provide a construction of associating a de Rham subbundle to a Higgs subbundle in characteristic $p$ in the geometric case. As applications, we obtain a Higgs semistability result and a $W_2$-unliftable result.

Pure mathematicsMathematics::Dynamical SystemsGeneral MathematicsHodge theoryHigh Energy Physics::PhenomenologyAlgebraMathematics - Algebraic GeometryMathematics::Algebraic GeometrySubbundleFOS: MathematicsHiggs bosonMathematics::Differential Geometry14F30 14F40Algebraic Geometry (math.AG)Mathematics::Symplectic GeometryMathematics
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Semistable Higgs bundles, periodic Higgs bundles and representations of algebraic fundamental groups

2019

Let $k $ be the algebraic closure of a finite field of odd characteristic $p$ and $X$ a smooth projective scheme over the Witt ring $W(k)$ which is geometrically connected in characteristic zero. We introduce the notion of Higgs-de Rham flow and prove that the category of periodic Higgs-de Rham flows over $X/W(k)$ is equivalent to the category of Fontaine modules, hence further equivalent to the category of crystalline representations of the \'{e}tale fundamental group $\pi_1(X_K)$ of the generic fiber of $X$, after Fontaine-Laffaille and Faltings. Moreover, we prove that every semistable Higgs bundle over the special fiber $X_k$ of $X$ of rank $\leq p$ initiates a semistable Higgs-de Rham …

Ring (mathematics)Pure mathematicsChern classApplied MathematicsGeneral MathematicsHodge theory010102 general mathematics01 natural sciencesAlgebraic closureHiggs bundleÉtale fundamental groupMathematics - Algebraic GeometryMathematics::Algebraic Geometryp-adic Hodge theoryMathematics::K-Theory and HomologyScheme (mathematics)FOS: Mathematics14D07 14F300101 mathematicsAlgebraic Geometry (math.AG)MathematicsJournal of the European Mathematical Society
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