Orateur
Description
In formal geometry, one naturally encounters complete algebras of
various kinds. This raises the question of how to deal with these
topological objects, at the derived level.
I will review two categorical frameworks which answer this question:
- the first one is that of Tate modules (introduced by Drinfeld
following Beilinson, and Hennion at the derived level);
- the second is the theory of solid modules of Clausen-Scholze, as part
of condensed mathematics.
Then I will explain the rather subtle relation between the two
(∞-)categories of modules. To conclude, I will mention some consequences
and first steps towards the theory of shifted symplectic structures in
such contexts.
This talk reports on joint work with Valerio Melani and Gabriele Vezzosi.