01:23:56
publiée le 6 juillet 2026
p-adic Eichler-Shimura theory - Lecture 3
De Vincent Pilloni , George Boxer
p-adic Eichler-Shimura theory - Lecture 1
Apparaît dans la collection : Jean Morlet Chair - Classical and p-adic aspects of the Kudla program / Chaire Jean Morlet - Aspects classiques et p-adiques du programme Kudla
Modular forms can be realized as Betti cohomology classes or coherent cohomology classes on modular curves. Eichler-Shimura theory compares both realizations. Using Betti realization, one can construct a first theory of p-adic automorphic forms : completed cohomology. Using the coherent realization we can construct another theory of p-adic automorphic forms : (higher) Coleman theory. Both theories compare, this is the p-adic Eichler-Shimura theory. In this course we will introduce several incarnations of the p-adic Shimura varieties (classical, perfectoid, locally analytic), as well as various period morphisms (Hodge-Tate and de Rham) and use this geometry to develop the theory of p-adic automorphic forms.
