Homological algebra of Frobenius-twisted polynomial superfunctors (Iacopo Giordano)

Orateur : Iacopo Giordano

Lieu : salle des Séminaires M3

Résumé :

The category P of polynomial functors was introduced by Friedlander and Suslin because these objects encode the homological information of polynomial GL_n - modules. Like for GL_n-modules, in characteristic p one can define the Frobenius twist F^(r) of a polynomial functor F. A theorem proved by Touzé and Chalupnik gives a natural formula relying the graded space Ext^*_P(F^(r), G^(r)) to the extensions of F and G. Our goal is to make the same computation in the more general context of Z/2-graded (=super) polynomial functors. Here we have more than one way to perform the Frobenius twist and, moreover, not all the techniques from the classical framework can be reproduced. We then investigate a Grothendieck spectral sequence in order to prove our results. This work was done was during my thesis at the Université de Lille under the supervision of Antoine Touzé.