2018
DOI: 10.1090/tran/7397
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Mumford curves covering đť‘ť-adic Shimura curves and their fundamental domains

Abstract: We give an explicit description of fundamental domains associated with the p-adic uniformisation of families of Shimura curves of discriminant Dp and level N ≥ 1, for which the one-sided ideal class number h(D, N ) is 1. The results obtained generalise those in [GvdP80, Ch. IX] for Shimura curves of discriminant 2p and level N = 1. The method we present here enables us to find Mumford curves covering Shimura curves, together with a free system of generators for the associated Schottky groups, p-adic good funda… Show more

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Cited by 2 publications
(4 citation statements)
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“…The classes of p-adic binary quadratic forms are obtained by the action of a discrete and cocompact subgroup of PGL 2 (Q p ) arising from the p-adic uniformization of the Shimura curve. We finally compute families of p-adic binary quadratic forms associated to an infinite family of Shimura curves studied in [2]. This extends results of Alsina-Bayer [1] to the p-adic context.…”
supporting
confidence: 56%
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“…The classes of p-adic binary quadratic forms are obtained by the action of a discrete and cocompact subgroup of PGL 2 (Q p ) arising from the p-adic uniformization of the Shimura curve. We finally compute families of p-adic binary quadratic forms associated to an infinite family of Shimura curves studied in [2]. This extends results of Alsina-Bayer [1] to the p-adic context.…”
supporting
confidence: 56%
“…Recall that Q p 2 Q p is the set of the Q p 2 -points of the p-adic upper-half plane H p (cf. [2] for a brief overview). We wish to underline the difference between Proposition 1.3 and its archimedean analog.…”
Section: Remark 12mentioning
confidence: 99%
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