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A Drinfeld module has a $\mathfrak{p}$-adic Tate module not only for every finite place $\mathfrak{p}$ of the coefficient ring but also for $\mathfrak{p} = \infty$. This was discovered by J.-K. Yu in the form of a representation of the Weil group. Following an insight of Taelman we give a construction of the $\infty$-adic Tate module by means of th...
Assuming everywhere good reduction we generalize the class number formula of Taelman to Drinfeld modules over arbitrary coefficient rings. In order to prove this formula we develop a theory of shtukas and their cohomology.
We show that unit $\mathcal{O}_{F,X}^\Lambda$-modules of Emerton and Kisin
provide an analogue of locally constant sheaves in the context of
B\"{o}ckle-Pink $\Lambda$-crystals. For example they form a tannakian category
if the coefficient algebra $\Lambda$ is a field. Our results hold for a big
class of coefficien algebras which includes Drinfeld r...
