Bruhat-Tits group scheme and parahoric torsor-2

Abstract: The aim of these lectures will be to introduce the notion of affine buildings and the notions of parahoric groups. The next aim will be to schematize these notions and get an overview of the structure of the Bruhat-Tits group schemes over discrete valuation rings. I will work entirely on the geometric case of the power series ring in one variable and the valuation ring there. In the last few lectures I will indicate applications of these concepts to the study of torsors on curves. The goal will be to understand the stack of parahoric torsors on smooth projective curves, relate them to the classical stack of parabolic bundles and prove a parahoric generalization of the Mehta-Seshadri theorem.

algebraic geometry

Audience: researchers in the topic

Algebraic Geometry at IIT Madras

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