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 …

Nonabelian Hodge theory in positive characteristic via exponential twisting

2015

On Hodge theory for the generalized geometry (I)

2013

Abstract We first investigate the linear Dirac structure from the viewpoint of a mixed Hodge structure. Then we discuss a Hodge-decomposition-type theorem for the generalized Kahler manifold and study the moduli space of a generalized weak Calabi–Yau manifold. We present a holomorphic anomaly equation and a one-loop partition function in a topological B-model under the generalized geometric context.