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 Post subject: Associated graded modulePosted: Tue, 17 Jan 2012 07:21:41 UTC
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Joined: Fri, 3 Sep 2010 09:29:45 UTC
Posts: 140
(A lot of what follows is from Matsumura - Commutative Ring Theory pp.174)

Let be a ring and A-module and an ideal of

Set

There are maps

for

which gives a map

I am interested in showing that, in a particular case, this is an isomorphism.

One of the conditions Matsumura gives for this is that
is flat over and
or (equivalently)
is flat over and

(Here and )

Now in the case I am interested in is a complete regular local Noetherian ring, so (letting I be the maximal ideal) is a field and so is flat over .

Is there anything in this particular case (complete local regular ring) that gives either or ? (I'm guessing the answer is no, and that is probably not true in general)

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