Phantom depth and flat base change

Details Phantom depth and flat base change Phantom depth and flat base change

2005-02-11

arxiv.org/abs/math/0502246v1

Proceedings of the American Mathematical Society, Volume 134, Number 2, February 2006, pp 313-321

Mathematics

Commutative Algebra

8 pages

Scientific paper

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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