Drinfeld Moduli Schemes and Automorphic Forms, 2013
The Theory of Elliptic Modules with Applications
SpringerBriefs in Mathematics Series

Drinfeld Moduli Schemes and Automorphic Forms: The Theory of Elliptic Modules with Applications is based on the author?s original work establishing the correspondence between ell-adic rank r Galois representations and automorphic representations of GL(r) over a function field, in the local case, and, in the global case, under a restriction at a single place. It develops Drinfeld?s theory of elliptic modules, their moduli schemes and covering schemes, the simple trace formula, the fixed point formula, as well as the congruence relations and a "simple" converse theorem, not yet published anywhere. This version, based on a recent course taught by the author at The Ohio State University, is updated with references to research that has extended and developed the original work. The use of the theory of elliptic modules in the present work makes it accessible to graduate students, and it will serve as a valuable resource to facilitate an entrance to this fascinating area of mathematics.

​ ​Elliptic Moduli.- Hecke Correspondences.- Trace Formulae.- Higher Recipropcity Laws. 

Provides a ?quick introduction to the Langlands correspondence for function fields via the cohomology of Drinfield moduli varieties Complete exposition of the theory of elliptic modules, their moduli schemes and covering schemes, as well as new congruence relations and a "simple" converse theorem Covers material that is known to experts and will be accesible to graduate students Includes supplementary material: sn.pub/extras