On the cuspidal divisor class group of a Drinfeld modular curve

  • Ernst-Ulrich Gekeler

    FB 9 Mathematik Universitat des Saarlandes Postfach 15 11 50 D-66041 Saarbrucken Germany
On the cuspidal divisor class group of a Drinfeld modular curve cover
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Abstract

The theory of theta functions for arithmetic groups that act on the Drinfeld upper half-plane is extended to allow degenerate parameters. This is used to investigate the cuspidal divisor class groups of Drinfeld modular curves. These groups are finite for congruence subgroups and may be described through the corresponding quotients of the Bruhat-Tits tree by . The description given is fairly explicit, notably in the most important special case of Hecke congruence subgroups over a polynomial ring.

Cite this article

Ernst-Ulrich Gekeler, On the cuspidal divisor class group of a Drinfeld modular curve. Doc. Math. 2 (1997), pp. 351–374

DOI 10.4171/DM/34