Etale Fundamental group of moduli of torsors under Bruhat-Tits group scheme over a curve

2019/11/07 by A. J. Parameswaran, Yashonidhi Pandey, Parameswaran, A. J. +1 · 2 citations
Mathematics · #14D20 #14D23 #14F22 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1911.02861

openalex publication_date 2019/11/07 · openalex created_date 2019/11/22 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth projective curve over an algebraically closed field k. Let G be a Bruhat-Tits group scheme on X which is generically semi-simple and trivial. We show that the étale fundamental group of the moduli stack M_X(G) of torsors under G is isomorphic to that of the moduli stack M_X(G) of principal G-bundles. For any smooth, noetherian and irreducible stack X, we show that an inclusion of an open substack X^∘, whose complement has codimension at least two, will induce an isomorphism of étale fundamental group. Over ℂ, we show that the open substack of regularly stable torsors in M_X(G) has complement of codimension at least two when g_X ≥ 3. As an application, we show that the moduli space M_X(G) of G-torsors is simply-connected.

Cited by

• On a theorem of Narasimhan and Ramanan on deformations
• Conformal blocks, parahoric torsors and Borel-Weil-Bott

Related

• Brauer group of moduli of torsors under Bruhat-Tits group scheme G over a curve
• Torsors on moduli spaces of principal G-bundles
• On tamely ramified \mathcal G-bundles on curves
• Moduli of parahoric \mathcal G--torsors on a compact Riemann surface
• Uniformization of G-bundles