Cohomology of twisted polynomial superfunctors through the twisting spectral sequence

TL;DR

This paper develops a spectral sequence approach to compute the cohomology of twisted polynomial superfunctors, revealing new insights into their Ext-spaces and generic cohomology in low degrees.

Contribution

It introduces a spectral sequence method to relate twisted and untwisted polynomial superfunctor cohomology, providing explicit low-degree computations.

Findings

Computed Ext-spaces for twisted polynomial superfunctors

Established relations between twisted and untwisted cohomology

Derived consequences for generic cohomology in low degrees

Abstract

We want to compute generic $\mathrm{Ext}$-spaces of twisted polynomial functors in relation to the $\mathrm{Ext}$-spaces of the untwisted ones, modulo a parametrisation. Thanks to the study of a spectral sequence we get to a computation in low degrees, with remarkable consequences at the level of generic cohomology.