Background & Purpose：

In 1974, Drinfeld introduced “elliptic modules”, called Drinfeld modules nowadays, to derive the Langlands correspondence for GL(2) over function fields. In the modern developments of the function field arithmetic, Drinfeld module plays a major role in various topics. Using “shtukas”, which is a generalized concept of Drinfeld modules, Lafforgue proved the Langlands correspondence for GL(n) over function fields. Meanwhile, Anderson’s “t-motives” (the “dual” of the higher dimensional Drinfeld modules) is a very powerful tool for the study of transcendence theory and “special L-values” in the context of equal characteristic.

This course is prepared for graduate students who are interested in the arithmetic of function fields and related topics. We will cover basic theories of Drinfeld modules, Drinfeld modular curves and t-motives etc. Recent developments around these topics will be also described. Students are required to have some backgrounds on algebraic number theory, algebraic function fields and non-archimedean analysis.