Bibliographic Details
| Title: |
The étale fundamental group of moduli of parahoric group scheme torsors over a curve. |
| Authors: |
Parameswaran, A J1 (AUTHOR), Pandey, Yashonidhi2 (AUTHOR) ypandey@iisermohali.ac.in |
| Superior Title: |
Proceedings of the Indian Academy of Sciences: Mathematical Sciences. Dec2023, Vol. 133 Issue 2, p1-27. 27p. |
| Subject Terms: |
*COMMERCIAL space ventures, *ISOMORPHISMS |
| Abstract: |
Let X be a smooth projective curve over an algebraically closed field k. Let G be an almost simple simply-connected group over k. Let G be a Bruhat–Tits group scheme on X which is generically the trivial group scheme with fibers G. 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. Our main goal is to prove that for any smooth, noetherian and irreducible stack X , the inclusion of any non-empty open substack X ∘ , whose complement has codimension at least two induces 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 over C the moduli space M X (G) of G -torsors is simply-connected. [ABSTRACT FROM AUTHOR] |
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