Condensed Learning Seminar

Quasi-coherent sheaves cannot support a six-functor formalism in the same way that e.g. \ell-adic sheaves do. Clausen and Scholze have shown that this can be fixed by extending the category of quasi-coherent sheaves to `solid sheaves’. In this talk we will sketch an alternative proof of this. We will define solid modules in a purely algebraic way (without reference to condensed mathematics), and produce f_! and f^! similarly to how it is done in SGA. This talk will be logically independent of the rest of the seminar. Based on a group project at the 2023 Stacks Project Workshop, with Emilie Arvidsson, Finn Bartsch, Thomas Brazelton, Sheela Devadas, Karim Réga, Gleb Terentiuk.