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Hashimoto, Mitsuyasu

Good filtrations and \(F\)-purity of invariant subrings. (English) Zbl 1222.13006

J. Math. Soc. Japan 63, No. 3, 815-818 (2011).
Summary: 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 \(S=\text{Sym}\,V\) has a good filtration, then \(S^U\) is \(F\)-pure.

Cited in 1 Document

MSC:

13A50 Actions of groups on commutative rings; invariant theory
13A35 Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure
14L24 Geometric invariant theory

Keywords:

good filtration; \(F\)-purity; invariant subring
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\textit{M. Hashimoto}, J. Math. Soc. Japan 63, No. 3, 815--818 (2011; Zbl 1222.13006)
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