Modular Form Congruences and Selmer Groups |
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Authors: | McGraw, William J. Ono, Ken |
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Affiliation: | Department of Mathematics, University of Wisconsin Madison WI 53706, USA, mcgraw{at}math.wisc.edu Department of Mathematics, University of Wisconsin Madison WI 53706, USA, ono{at}math.wisc.edu |
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Abstract: | Motivated by Cremona and Mazur's notion of visibility of elementsin ShafarevichTate groups [6, 27], there have been anumber of recent works which test its compatibility with theBirch and SwinnertonDyer conjecture and the BlochKatoconjecture. These conjectures provide formulas for the ordersof ShafarevichTate groups in terms of values of L-functions.For example, one may see recent work of Agashe, Dummigan, Steinand Watkins [1, 2, 10, 11]. In their examples, they find thatthe presence of visible elements agrees with the expected divisibilityproperties of the relevant L-values. |
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