Drinfeld modules

The Carlitz module

The seminar was held during the winter semester 2015. Its aim was to understand the results of Lenny Taelman on special values of Goss L-functions attached to Drinfeld modules.

Talks

23-09-15

Organizational meeting

30-09-15

Class number formula for global fields

07-10-15

Introduction to Drinfeld modules

14-10-15

Goss L-functions I

21-10-15

Goss L-functions II
(notes for both talks: pdf)

28-10-15

Explicit class field theory

18-11-15

Irrationality and transcendence of special values

25-11-15

Class number formula I

16-12-15

Class number formula II

Organizers

Pasha Solomatin <p.solomatin@math.leidenuniv.nl>
Maxim Mornev <m.mornev@math.leidenuniv.nl>

The organizers of the seminar

Approximate program

Introduction: class number formula for global fields, special values of classical L-functions and their irrationality.

Drinfeld modules and their analytic uniformization.

Goss L-functions.

Explicit class field theory.

Taelman's class number formula.

Irrationality of special values in positive characetristic.

Uniformization via Drinfeld shtukas.

References

G. Anderson. t-Motives. Duke Math. J. 53 (1986), no. 2, 457–502.

P. Deligne, D. Husemöller. Survey of Drinfeld modules, in: Current Trends in Arithmetical Algebraic Geometry (Arcata, Calif., 1985). Contemporary mathematics 67 (1987), 25–91.

V. Drinfeld. Elliptic modules. Math. USSR-Sb. 23 (1974), no. 4, 561–592.

V. Drinfeld. Elliptic modules, II. Math. USSR-Sb. 31 (1977), no. 2, 159–170.

D. Goss. Basic structures of function field arithmetic. Springer (1998)

D. Goss. v-adic zeta functions, L-series and measures for function fields. Invent. Math. 55 (1979), no. 2, 107–119.

D. Goss. On a new type of L-function for algebraic curves over finite fields. Pacific J. Math. 105 (1983), no. 1, 143–181.

B. Lutes. Special values of the Goss L-function and special polynomials. PhD thesis. Texas A&M (2010)pdf

R. Perkins. What is Anderson's log-algebraicity? (2013)pdf

R. Perkins. On special values of Pellarin's L-series. PhD thesis. OSU (2013)

L. Taelman. A Dirichlet unit theorem for Drinfeld modules. Math. Ann. 348 (2010), no. 4, 899–907.

L. Taelman. Special L-values of Drinfeld modules. Ann. Math. 175 (2012), no. 1, 369–391.

L. Taelman. The Carlitz shtuka. J. Number Theory 131 (2011), no. 3, 410–418.

L. Taelman. Sheaves and functions modulo p, lectures on the Woods-Hole trace formula. LMS Lecture Note Series, volume 429 (2015)pdf

D. Thakur. On characteristic p zeta functions. Compositio Math. 99 (1995), no. 3, 231–247.

D. Zywina. Explicit class field theory for global function fields. (2011)

Last modified: April 19, 2019.