Mitsuyasu Hashimoto
Good filtrations and $F$-purity of invariant subrings.
Fri, 10/02/2009 - 09:41 — SomNambulAuthors: Mitsuyasu Hashimoto
Subjects: Commutative Algebra
AbstractLet $k$ 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.$F$-pure homomorphisms, strong $F$-regularity, and $F$-injectivity.
Thu, 08/20/2009 - 23:06 — SomNambulAuthors: Mitsuyasu Hashimoto
Subjects: Commutative Algebra
AbstractWe discuss Matijevic-Roberts type theorem on strong $F$-regularity,
$F$-purity, and Cohen-Macaulay $F$-injective (CMFI for short) property. Related
to this problem, we also discuss the base change problem and the openness of
loci of these properties. In particular, we define the notion of $F$-purity of
homomorphisms using Radu-Andre homomorphisms, and prove basic properties of it.
We also discuss a strong version of strong $F$-regularity (very strong
$F$-regularity), and compare these two versions of strong $F$-regularity.
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