Fundamental Groups in Arithmetic and Algebraic Geometry

# Semistable Higgs bundles and representation of fundamental groups over mixed characteristic

speaker: Kang Zuo (Johannes Gutenberg Universität Mainz)

abstract: I shall report my recent work joint with G-T. Lan and M. Sheng on semistable Higgs bundles over a smooth projective schmeme $XW(k)$ and crytallien sheaves on the the generic fibre of $X$. We define the inverse Cartier's transform on a certain subcategory of Higgs bundles over $XWn(k)$, which recovers the characteristic $p$ case due to Ogus-Vologodsky. We then introduce the notions: p-adic Higgs-de Rham flow, preperiodic Higgs bundles and strongly semistable Higgs bundles. We discuss the relation between the category of semistable Higgs bundles and the category of crystallien sheaves via those intermediante categories. If the time is allowed, I shall explain how our work (joint with Y-H. Yang) can be applied in S. Mochizuki's work on $p$-adic Teichmueller Theory.

timetable:
Tue 17 Dec, 16:30 - 17:30, Aula Dini
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