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Title:听Semistability of G-torsors and integration questions in characteristic p>0

础产蝉迟谤补肠迟:听Constructing quotients is a natural but difficult question in algebraic geometry. A key tool for this purpose is the notion of semistability. Let k be a field and X be a k-curve. Let also G be a reductive group over X obtained from a reductive group over k by base change. Semistability for G-torsors can be defined by several ways. In this talk we present Atiyah--Bott and Behrend's approaches. We then explain why the first approach can be extended to some positive characteristics and why both of these approaches lead to the same notion (when they are both well-defined). For this, I established during my PhD an analogue in positive characteristic of a theorem of Morozov, which classifies, in characteristic 0, parabolic subalgebras of a reductive group by means of their nilradical.

In the second part of the talk, I will present this analogue and detail some of the positive characteristic issues its proof raised. More specifically, I will focus on integration questions for nil algebras in this context: roughly speaking I will discuss the existence of a map that plays the role of the exponential map (defined by its power series), even in small characteristics.

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Qu茅bec-Vermont Number Theory Seminar
Web - For details, please contact: martinez [at] crm.umontreal.ca

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