Torsors on Affine Varieties

2014/04/01 by S. Subramanian, Subramanian, S.
Engineering · Mathematics · #14-XX #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Tensor decomposition and applications #math.AG #msc:14-XX

paper · pdf · doi:10.48550/arxiv.1404.0143

Revised version

openalex publication_date 2014/04/01 · arxiv created 2015/07/27 · arxiv updated 2015/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth affine algebraic variety over the field of complex numbers which is contractible. Then every algebraic G-torsor on X is algebraically trivial if G is a semi-simple algebraic group. We also show that if X is a smooth affine algebraic variety such that Ω¹_X is trivial and X is topologically simply connected with Hⁱ(X,\mathbb Z)=0 for i=1,2 and 3, then every algebraic G-torsor on X is algebraically trivial for a semi-simple algebraic group G.

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