Sesquilinear pairings on elliptic curves

Katherine E. Stange

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arXiv · 2405.14167

Sesquilinear pairings on elliptic curves

Katherine E. Stange

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Abstract

Let $E$ be an elliptic curve with complex multiplication by a ring $R$, where $R$ is an order in an imaginary quadratic field or quaternion algebra. We define sesquilinear pairings ($R$-linear in one variable and $R$-conjugate linear in the other), taking values in an $R$-module, generalizing the Weil and Tate-Lichtenbaum pairings.

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Katherine E. Stange. 2024-05-23. Sesquilinear pairings on elliptic curves. https://arxiv.org/abs/2405.14167

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