A presentation theorem for smooth projective schemes over discrete valuation rings

2023/02/06 by Ning Guo, Guo, Ning, Ivan Panin +1
Mathematics · #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.2302.02818

openalex publication_date 2023/02/06 · openalex created_date 2023/02/09 · openalex updated_date 2026/07/28

Abstract

In this article, we give a proof for a geometric presentation theorem for any irreducible scheme X smooth projective over a discrete valuation ring R. As a consequence, for any reductive R-group scheme G, we prove that any generically trivial principal G-bundle over X glued to a principal G_U-bundle over the affine line \mathbbA¹_U for a semilocal affine scheme U.

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