A remark on torsors for affine group schemes
Michael Wibmer
TL;DR
This paper provides an elementary proof that all torsors for affine group schemes over algebraically closed fields are trivial, connecting to the uniqueness of fibre functors in neutral tannakian categories.
Contribution
It offers a simplified proof of torsor triviality for affine group schemes, enhancing understanding of tannakian categories and their fibre functors.
Findings
All torsors for affine group schemes over algebraically closed fields are trivial.
The proof relates torsor triviality to the uniqueness of fibre functors.
Clarifies the structure of neutral tannakian categories.
Abstract
We present an elementary proof of the fact that every torsor for an affine group scheme over an algebraically closed field is trivial. This is related to the uniqueness of fibre functors on neutral tannakian categories.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology