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$F$-pure homomorphisms, strong $F$-regularity, and $F$-injectivity | Mitsuyasu Hashimoto
; | Date: |
19 Aug 2009 | Abstract: | We 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. As a
result, strong $F$-regularity and very strong $F$-regularity agree for local
rings, $F$-finite rings, and essentially finite-type algebras over an excellent
local rings. We prove the $F$-pure base change of strong $F$-regularity. | Source: | arXiv, 0908.2703 | Services: | Forum | Review | PDF | Favorites |
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