The refined class number formula for Drinfeld modules

Abstract

Let $K/k$ be a finite Galois extension of global function fields. Let $E$ be a Drinfeld module over $k$. We state and prove an equivariant refinement of Taelman's analogue of the analytic class number formula for $(E,K/k)$, and derive explicit consequences for the Galois structure of the Taelman class group of $E$ over $K$.

Final version, to appear in Compositio Mathematica. 53 pages