Lucas Mann, Humboldt Universität zu Berlin
Wednesday, December 12, 2018 - 11:15
Humboldt-Universität zu Berlin, Institut für Mathematik
Rudower Chaussee 25, 12489 Berlin, R. 2006
FS Algebra und Zahlentheorie
Prof. E. Große-Klönne
Motivated by the comparison of different cohomology theories on p-adic varieties, Scholze introduced a q-analogue of the classical de Rham complex which interpolates between de Rham structures and étale structures. We study the relative theory in that context, i.e. the q-analogue of connections. In the first part of the talk we present fundamental properties of the category of q-connections in a very general setting, showing that this category satisfies similar properties as the category of classical connections. The second part is devoted to the p-adic version of the theory; we construct a p-adic Riemann- Hilbert functor which transforms q-connections to étale ZP-local systems. One of the main ingredients of the second part is the relative p-adic Hodge theory developed by Kedlaya and Liu, which provides us with a vast generalization of the classical (φ,Γ)- correspondence.
submitted by Zyska (zyska@math.hu-berlin.de, [030] 20931812)