General information: In this study group, we are going to learn about the construction of eigenvarieties. We shall start with basic discussions on nonarchimedean functional analysis. The preparation of nonarchimedean functional analysis then allows one to construct the so-called spectral variety. Then, we shall learn about Buzzard's eigenvariety machinery. At the end of the study group, we shall see how eigenvarieties are used in modern number theory. This study group is co-organised with Muhammad Manji.
Time: Thursdays, 3 pm
Room: B1.01
Schedule
Talk 1 (12. Jan.): Introduction. Speaker: Ju-Feng
Talk 2 (19. Jan): Nonarchimedean functional analysis (over a nonarchimedean field). Speaker: Alex
Banach modules, Buzzard's (Pr) condition, compact operators.
Talk 3 (26. Jan.): Nonarchimedean functional analysis (over an affinoid algebra). Speaker: Muhammad
Banach modules, Buzzard's (Pr) condition, compact operators.
Talk 4 (02. Feb.): Fredholm determinant and the spectral variety. Speaker: Arshay
Fredholm determinant, slope decomposition, spectral varieties.
Talk 5 (09. Feb.): Buzzard's eigenvariety machinery. Speaker: Arshay
Buzzard's eigenvariety machinery, properties of eigenvarieties.
Talk 6 (16. Feb.): Stevens's overconvergent modular symbols I. Speaker: James
Classical and overconvergent modular symbols, Eichler--Shimura decomposition, Stevens's control theorem.
Talk 7 (23. Feb.): Stevens's overconvergent modular symbols II. Speaker: James
Classical and overconvergent modular symbols, Eichler--Shimura decomposition, Stevens's control theorem.
Talk 8 (02. Mar.): Application to p-adic L-functions. Speaker: Pak-Hin (cancelled)
Reference
Joël Bellaïche (2021), The Eigenbook
Kevin Buzzard (2010), Eigenvarieties
Judith Ludwig (2020), Topics in the theory of adic spaces and the Eigenvariety machine
Jean-Pierre Serre (1962), Endomorphismes complètement continus des espaces de Banach p-adiques