Evolutions, Symbolic Squares, and Fitting Ideals
| dc.creator | Eisenbud, David | |
| dc.creator | Mazur, Barry | |
| dc.date | 1995-11-15 | |
| dc.date.accessioned | 2026-07-07T09:06:38Z | |
| dc.date.available | 2026-07-07T09:06:38Z | |
| dc.description | 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 $Ω_{R/k}\otimes T \to Ω_{T/k}$. 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. | |
| dc.description | plain tex | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9511008 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9511008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150084 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.title | Evolutions, Symbolic Squares, and Fitting Ideals | |
| dc.type | text |