Phantom depth and flat base change

We prove that if $f: (R,\m) \to (S,\n)$ is a flat local homomorphism, $S/\m S$ is Cohen-Macaulay and $F$-injective, and $R$ and $S$ share a weak test element, then a tight closure analogue of the (standard) formula for depth and regular sequences across flat base change holds. As a corolla...

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Veröffentlicht in:	arXiv.org 2005-02
1. Verfasser:	Epstein, Neil M
Format:	Artikel
Sprache:	eng
Schlagworte:	Homomorphisms
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description	We prove that if $f: (R,\m) \to (S,\n)$ is a flat local homomorphism, $S/\m S$ is Cohen-Macaulay and $F$-injective, and $R$ and $S$ share a weak test element, then a tight closure analogue of the (standard) formula for depth and regular sequences across flat base change holds. As a corollary, it follows that phantom depth commutes with completion for excellent local rings. We give examples to show that the analogue does not hold for surjective base change.
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title	Phantom depth and flat base change
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