Number Theory Seminar: Pro-étale quasicoherent cohomology of negative Banach–Colmez spaces

Negative Banach–Colmez spaces are moduli spaces of extensions of vector bundles on the Fargues–Fontaine curve. They play important roles in the Fargues–Scholze program and p-adic local Langlands. In this talk, I will discuss how to use the newly developed 6-functor formalism of pro-étale quasicoherent cohomology to compute the cohomology of negative Banach–Colmez spaces. Along this way, I will also show some tools such as Drinfeld’s lemma which are of more general interest. This is based on the joint work with people from last year’s AIM workshop on chromatic homotopy theory and p-adic geometry.
In the pretalk, I will give an introduction to pro-étale cohomology and to Poincaré duality for rigid-analytic spaces.