Posts Tagged ‘Krull-Akizuki’

Krull-Akizuki, the Amitsur complex

March 19, 2011

These are some of the few recent additions. Krull-Akizuki is nice because it implies that (I didn’t know this before) the integral closure of a Dedekind domain in any finite extension, not necessarily separable, is Dedekind. One of the applications that should eventually appear is that a noetherian local domain can always be dominated by a DVR (as opposed to just a plain valuation ring).

The Amitsur complex is what Tamme calls it; others just write  it out. This is the sequence that you get for a faithfully flat extension of rings, whose exactness is what leads to all sorts of descent theorems, which will someday appear here. (There is a MathOverflow question on the history of it.)

Advertisements