Séminaire Combinatoire et Théorie des Nombres ICJ
# Shtuka cohomology and special values of Goss L-functions (2)

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Bât. Braconnier, salle séminaire 2 (ICJ, Université Lyon 1)
### Bât. Braconnier, salle séminaire 2

#### ICJ, Université Lyon 1

Description

Shtuka models of Drinfeld modules and their cohomology.

Abstract.

Taelman discovered an analog of BSD conjecture for Drinfeld modules and

proved it for the coefficient ring F_q[t]. His methods do not generalize

easily to more complicated rings. A different approach to Taelman's BSD

conjecture is provided by the theory of shtuka cohomology. This approach

allows one to treat all the coefficient rings in a uniform way. It leads

to a rather conceptual proof of the conjecture which resonates well with

equivariant Tamagawa number conjecture for motives.

My aim is to explain the shtuka-theoretic proof of Taelman's analog

of the BSD conjecture. The course can be naturally divided into three

parts:

1. Statement of the conjecture, overview of the proof and introduction to shtuka cohomology.

2. Shtuka models of Drinfeld modules and their cohomology.

3. Regulator theory and trace formula for elliptic shtukas.