Phantom depth and flat base change

Epstein, Neil

doi:10.1090/S0002-9939-05-08223-7

Phantom depth and flat base change
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by Neil M. Epstein PDF

Proc. Amer. Math. Soc. 134 (2006), 313-321 Request permission

Abstract:

We prove that if $f: (R,\mathfrak {m}) \rightarrow (S,\mathfrak {n})$ is a flat local homomorphism, $S/\mathfrak {m} S$ 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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