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Proceedings of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0972230-7
PII: S 0002-9939(1989)0972230-7
Article copyright: © Copyright 1989 American Mathematical Society