中科院数学与系统科学研究院
数学研究所
中科院华罗庚数学重点实验室
华罗庚青年数学论坛
学术报告
报告人：张驷庆（Institute for Advanced Study）
题目：NonAbelian Hodge Theory in prime characteristics I: semistability and cohomology
时间：2024.06.04（星期二），10:00-11:00
地点：MCM 410
摘要：The Non Abelian Hodge Theory for a curve in characteristic p relates themoduli of flat connections on the curve and the moduli of Higgs bundles on theFrobenius twist of the curve. Previously, it is known that both moduli stacks sit over a Hitchinbase, and that they differ by a twist of a torsor under a Picard stack over theHitchin base. Now we know that, by shrinking the Picard stack and its torsorsimultaneously, we can make the twist respect semistability. Consequently, thesemistable Dolbeault and de Rham moduli spaces differ by a twist of a torsorunder a connected group scheme over the Hitchin base. We then deduce someresults on the cohomologies of the moduli spaces, some of which entail newresults in characteristic zero. Based on joint works with Mark de Cataldo andMichael Groechenig.
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报告人：张驷庆（Institute for Advanced Study）
题目：NonAbelian Hodge Theory in prime characteristic II: log-poles and G-bundles
时间：2024.06.11（星期二），09:00-10:00
地点：MCM 410
摘要：The previous talk is about Higgs fields and flatconnections on vector bundles. In the first half of this talk, we consider howthe picture changes when we add log poles. It turns out that the de Rham modulispace is, up to a twist and over an open of the Hitchin base, a Galois cover ofthe Dolbeault moduli space. This happens due to a curious appearance of theArtin-Schreier map on the residues. In the second half of this talk, weconsider the case with G-bundles and no poles. We show that the analogousresults on semistability and cohomology also hold. This relies on a detailedstudy of Ngo’s regular centralizers, and the theory of Theta-semistability.Based on joint works with Mark de Cataldo and Andres Fernandez Herrero.
