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Proceedings of the American Mathematical Society

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Mumford curves with maximal automorphism group

Authors: Gunther Cornelissen and Fumiharu Kato
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Journal: Proc. Amer. Math. Soc. 132 (2004), 1937-1941
MSC (2000): Primary 14H37, 14G22
Published electronically: January 30, 2004
MathSciNet review: 2053963
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Abstract: A Mumford curve of genus $g \notin \{0,1,5,6,7,8 \}$ over a non-Archimedean valued field of characteristic $p>0$ has at most $ 2 \sqrt{g} (\sqrt{g}+1)^2 $ automorphisms. In this note, the unique family of curves that attains this bound, and its automorphism group, are determined.

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Additional Information

Gunther Cornelissen
Affiliation: Mathematisch Instituut, Universiteit Utrecht, Postbus 80.010, 3508 TA Utrecht, Nederland

Fumiharu Kato
Affiliation: Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan

Received by editor(s): December 21, 2000
Received by editor(s) in revised form: April 18, 2003
Published electronically: January 30, 2004
Additional Notes: This work was done when the first author was visiting Kyoto University. The main result of this paper answers positively a question posed by T. Sekiguchi during the 2000 Kinosaki Symposium on Algebraic Geometry
Communicated by: Michael Stillman
Article copyright: © Copyright 2004 American Mathematical Society