Where can I found a description of the deformation theory for modules?Is it possible to deform a free module in such way that each fibre of the deformation is still free?
1 Answer
$\begingroup$
$\endgroup$
3
A free module is rigid, because $Ext^1(E, E)=0$ for any free module $E.$ For deformation theory see for example ``Functors of Artin Rings'' by Michael Schlessinger.
-
3$\begingroup$ Well, this certainly depends. If $E$ is an $R$-module and you want to deform it as an $R$-module, then it's rigid. But often it happens that a module is free over some $S$ but you want to deform it over some other $R$. In that case the deformation problem is not rigid. By the way, I'm not so sure Schlessinger's paper handles the case of modules, but I may have a faulty recollection here. $\endgroup$ May 1, 2010 at 12:02
-
$\begingroup$ Oh, and do a MathScinet search of deformations of modules and you will likely get hundreds of hits. $\endgroup$ May 1, 2010 at 12:04
-