On the variation of Tate-Shafarevich groups of elliptic curves over hyperelliptic curves |
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Authors: | Mihran Papikian |
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Institution: | Department of Mathematics, Stanford University, Stanford, CA 94305, USA |
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Abstract: | Let E be an elliptic curve over F=Fq(t) having conductor (p)·∞, where (p) is a prime ideal in Fqt]. Let d∈Fqt] be an irreducible polynomial of odd degree, and let . Assume (p) remains prime in K. We prove the analogue of the formula of Gross for the special value L(E⊗FK,1). As a consequence, we obtain a formula for the order of the Tate-Shafarevich group Ш(E/K) when L(E⊗FK,1)≠0. |
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Keywords: | primary 11G05 11G40 secondary 11G18 |
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