KIAS Intensive Lecture Series on Shimura varieties and Rapoport-Zink spaces
Perfectoid spaces and Rapoport-Zink space at infinite level(Lec. 3)
SPEAKER | Yoichi Mieda
INSTITUTE | Kyoto
DATE | January 15(Wed), 2014
TIME | 10:00
PLACE | 1503 Conference room, KIAS
ABSTRACT | Motivatied mainly by the global and local Langlands correspondence, we are interested in the I-adic etale cohomology of Shimura varieties (e.g. the modular curve) and Rapoport-Zink spaces (e.g. the Lubin-Tate space). They are towers (i.e. projective systems indexed bt levels) of algebraic varieties and rigid analytic spaces, respectively. Sometimes it is crucial to consider their "limits", namely, the spaces at infinite level. For example, the Hecke operators, being algebraic correspondences at finite level, become a group action at infinite level. More serious example is the Faltings-Fargues isomorphism between the Lubin-Tate space and the Drinfeld space at infinite level. This isomorphism does not descend to a finite level, so passing to infinite level is essential.