The objective of the reading course is to understand recent progress in the study of completed cohomology of Shimura varieties. The main references are the following articles:
Lue Pan, On locally analytic vectors of the completed cohomology of modular curves
Vincent Pilloni, Faisceaux equivariants et faisceaux automorphes
Juan Esteban Rodriguez Camargo, Locally analytic completed cohomology
We will meet on non-QVNTS Thursdays in the conference room LB 921-4 in the LB building at Concordia, usually at 2pm but some days a bit later. Please see below for the detailed schedule.
September 21st, 14:00 A. Iovita Introduction I: Overview of the main results in the articles quoted. p-Adic Galois representations and classical Sen theory.
October 19th, 15:00 A. Iovita Introduction II: The completed cohomology of a p-adic tower of modular curves and its Sen-theory.
November 2nd, 14:00 T. Leblanc The perfectoid tower of modular curves and the Hodge-Tate map.
November 16th, 15:00 G.Rosso Completed cohomology, the Jacquet functor, and the description of completed cohomology in terms of the flag variety.
November 30th, 14:00 H. Fu Locally analytic vectors.
January 11th, 10:00 A. Kazi Relative Sen theory I.
January 11th, 14:00 A. Iovita Relative Sen theory II.
February 8th, 10:00 TBD Relative Sen theory applied to modular curves. The relative Sen operator.
February 8th, 14:00 TBD Applications to the Hodge-Tate theory of completed cohomology.
February 22nd, 10:00 TBD Equivariant sheaves and automorphic sheaves (following Pilloni).
TBD Higher dimensional variants (following Juan Esteban).