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Analogue of the degree conjecture over function fields
Author(s):
Mihran
Papikian
Journal:
Trans. Amer. Math. Soc.
359
(2007),
3483-3503.
MSC (2000):
Primary 11G05;
Secondary 11G18
Posted:
February 13, 2007
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Abstract:
Under a certain assumption, similar to Manin's conjecture, we prove an upper bound on the degree of modular parametrizations of elliptic curves by Drinfeld modular curves, which is the function field analogue of the conjectured bound over the rational numbers.
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Additional Information:
Mihran
Papikian
Affiliation:
Department of Mathematics, Stanford University, Stanford, California 94305
Email:
papikian@math.stanford.edu
DOI:
10.1090/S0002-9947-07-04147-5
PII:
S 0002-9947(07)04147-5
Keywords:
Degree conjecture,
Drinfeld modular curves,
ABC conjecture,
monodromy pairing
Received by editor(s):
October 27, 2004
Received by editor(s) in revised form:
July 26, 2005
Posted:
February 13, 2007
Additional Notes:
This research was supported by a fellowship from the European Postdoctoral Institute
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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