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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A $p$-adic analogue of the Gauss-Bonnet theorem for certain Mumford curves

Author: Richard M. Freije
Journal: Proc. Amer. Math. Soc. 107 (1989), 323-332
MSC: Primary 11G20; Secondary 14G20
MathSciNet review: 972230
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Abstract: If $K$ is a local field, $L$ a quadratic extension, $\Gamma$ a Schottky group co-compact in ${\text {PG}}{{\text {L}}_2}(K)$ then the quotient $L - K/\Gamma$ corresponds to the $L$-points of a Mumford curve. In this paper we calculate $\int _{L - K/\Gamma } {d\mathcal {M}}$ where $\mathcal {M}$ is an ${\text {PG}}{{\text {L}}_2}(K)$ invariant measure on $L - K$, in terms of the genus of the corresponding curve.

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Article copyright: © Copyright 1989 American Mathematical Society