2025/2026

Motives and L-functions

Type: Optional course (faculty)

Delivered by: Faculty of Mathematics

When: 1, 2 module

Open to: students of all HSE University campuses

Language: English

Contact hours: 30

Course Syllabus

Abstract

Grotendieck originally introduced the idea of ​​a ""motif"" in a letter to Serre in the early 1960s. Motives are interesting in their own right and much is still unknown about them, as indicated for instance by Grothendieck's ""standard conjectures"". On the other hand an L-function is a holomorphic function which encodes certain properties of an arithmetic-geometric object (e.g. a finite type scheme over a number field or a motive). The classical Riemann-zeta function is perhaps the earliest example of an L-function. In this course we will discuss Deligne's conjecture (and it's variants e.g. Bloch-Kato) which is a statement relating the values ​​of L-functions at integer points (so called special values) to the ""regulator"" of the motive. This is a vast generalization of the classical class number formula.