Finiteness theorems and obstructions for deformations of complexes

Lundi 13 octobre 2008 10:30-11:30 - Chinburg Ted - University of Pennsylvania

Résumé : This is a report on some work with Frauke Bleher and Luc Illusie on a generalization to complexes of the deformation theory of Mazur and Schlessinger for modules for a profinite group. A new question arises when deforming complexes : Is the versal deformation represented by a bounded complex of modules which are each finitely generated over the versal deformation ring ? We will describe some evidence that this is the case when the complex arises from arithmetic. We will also describe a construction by O. Gabber of a lifting obstruction in the expected Ext^2 group. This construction turns out to have a nice relation to the sequence of low degree terms associated to the next to last term in the filtration of a spectral sequence.

Lieu : 425 - petit amphi

Finiteness theorems and obstructions for deformations of complexes  Version PDF