Evolutions, Symbolic Squares, and Fitting Ideals

Details Evolutions, Symbolic Squares, and Fitting Ideals Evolutions, Symbolic Squares, and Fitting Ideals

1995-11-15

arxiv.org/abs/alg-geom/9511008v1

Mathematics

Commutative Algebra

plain tex

Scientific paper

Given a reduced local algebra $T$ over a suitable ring or field $k$ we study the question of whether there are nontrivial algebra surjections $R\to T$ which induce isomorphisms $\Omega_{R/k}\otimes T \to \Omega_{T/k}$. Such maps, called evolutions, arise naturally in the study of Hecke algebras, as they implicitly do in the recent work of Wiles, Taylor-Wiles, and Flach. We show that the existence of non-trivial evolutions of an algebra $T$ can be characterized in terms of the symbolic square of an ideal defining $T$. We give a characterization of the symbolic square in terms of Fitting ideals. Using this and other techniques we show that certain classes of reduced algebras -- codimension 2 Cohen-Macaulay, Codimension 3 Gorenstein, licci algebras in general, and some others -- admit no nontrivial evolutions. On the other hand we give examples showing that non-trivial evolutions of reduced Cohen-Macaulay algebras of codimension 3 do exist in every positive characteristic.

Affiliated with

Also associated with

No associations

Rating

Evolutions, Symbolic Squares, and Fitting Ideals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Evolutions, Symbolic Squares, and Fitting Ideals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Evolutions, Symbolic Squares, and Fitting Ideals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-112834