Thời gian: 16h30 thứ năm, ngày 11/05/2023

Địa điểm: Pòng 612, Nhà A6.

Link online: https://meet.google.com/yep-kbzk-eao?pli=1&authuser=4

Tóm tắt: In this talk, I will recall some deep results of Drinfeld ([Dri04]) on fpqc-local nature of the projectivity of modules over a Laurent series ring. These descent results are generalizations of a theorem of Raynaud-Gruson ([GR71]) which says that the property of a module being projective can be checked fpqc-locally. To state the results, we also need to introduce Tate modules and some related definitions. As an application, we can show that certain natural moduli stacks of local Galois representations are algebraic (or Ind-algebraic) stacks (see [EG19]).

References:

• [Dri04] Vladimir Drinfeld, Infinite-dimensional vector bundles in algebraic geometry: an introduction, The unity of mathematics, Progr. Math., vol. 244, Birkhauser Boston, Boston, MA, 2006.
• [EG19] Matthew Emerton and Toby Gee, Scheme-theoretic images of certain morphisms of stacks,  Journal of Algebraic Geometry (2019).
• [GR71] Michel Raynaud and Laurent Gruson, Crit`eres de platitude et de projectivité. Techniques de planification d' un module, Invent. Math. 13 (1971)