Good filtrations and F-purity of invariant subrings

2009/10/01 by Mitsuyasu Hashimoto, Hashimoto, Mitsuyasu
Mathematics · #13A35 #13A50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0910.0081

openalex publication_date 2009/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be an algebraically closed field of positive characteristic, G a reductive group over k, and V a finite dimensional G-module. Let B be a Borel subgroup of G, and U its unipotent radical. We prove that if S=\Sym V has a good filtration, then S^U is F-pure.

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