2025/2026
Геометризация программы Ленглендса
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
3, 4 модуль
Охват аудитории:
для всех кампусов НИУ ВШЭ
Преподаватели:
Гайсин Ильдар Маратович
Язык:
английский
Кредиты:
3
Контактные часы:
36
Course Syllabus
Abstract
In the last 5 years, there has been a considerable amount of work led by Peter Scholze, Laurent Fargues and various colleagues to extend the classical (l-adic/real) local Langlands correspondence to a geometric version.
In this course we will provide an overview of the main actors appearing in both the l-adic and real versions. This will include a stack of G-bundles representing the analytic side (i.e. automorphic representations) and a stack of L-parameters representing the number theoretic side (i.e. Galois representations).
Expected Learning Outcomes
- The aim of the course is to construct the Fargues–Fontaine curve X and the stack of G-bundles, so that the conjecture above can be properly formulated
Course Contents
- Review of adic-spaces and etale cohomology Examples: The Fargues – Fontaine curve
- Stack of G-bundles. Beilinson–Drinfeld Grassmannian Examples: Geometric – Satake correspondence
- Stack of L-parameters. Formulation of the conjecture.
Interim Assessment
- 2025/2026 4th moduleexam format: oral examination at the end of the course. grading formula = 1.0*F (i.e. completely based on the oral exam)
Bibliography
Recommended Core Bibliography
- Bhatt, B., & Scholze, P. (2019). Prisms and Prismatic Cohomology. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1905.08229
- Edidin, D. (2010). Equivariant geometry and the cohomology of the moduli space of curves. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1006.2364
Recommended Additional Bibliography
- Scholze, P. (2010). The Local Langlands correspondence for $\GL_n$ over $p$-adic fields. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1010.1540