\(p\)-adic \(L\)-functions and Selmer varieties associated to elliptic curves with complex multiplication (Q990188)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(p\)-adic \(L\)-functions and Selmer varieties associated to elliptic curves with complex multiplication |
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\(p\)-adic \(L\)-functions and Selmer varieties associated to elliptic curves with complex multiplication (English)
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6 September 2010
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The principle of Birch and Swinnerton-Dyer states that nonvanishing of \(L\)-values accounts in some appropriate sense for the finiteness of integral points. The author aims at extending these ideas to hyperbolic curves. The present paper discusses the special case of a hyperbolic curve of genus 1 over \(\mathbb{Q}\) obtained from an elliptic curve over \(\mathbb{Q}\) with complex multiplication by removing the origin.
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elliptic curve
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complex multiplication
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Selmer variety
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Birch-Swinnerton-Dyer conjecture
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L-function
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