Journal of the Mathematical Society of Japan

Good filtrations and F-purity of invariant subrings


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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 $S = \mathrm{Sym} \: V$ has a good filtration, then $S^U$ is $F$-pure.

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J. Math. Soc. Japan, Volume 63, Number 3 (2011), 815-818.

First available in Project Euclid: 1 August 2011

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Zentralblatt MATH identifier

Primary: 13A50: Actions of groups on commutative rings; invariant theory [See also 14L24]
Secondary: 13A35: Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p; tight closure [See also 13B22]

good filtration F-pure invariant subring


HASHIMOTO, Mitsuyasu. Good filtrations and F -purity of invariant subrings. J. Math. Soc. Japan 63 (2011), no. 3, 815--818. doi:10.2969/jmsj/06330815.

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