We define sesquilinear (conjugate linear) pairings generalizing the Weil and Tate-Lichtenbaum pairings on elliptic curves. Specifically, on elliptic curves with complex multiplication by a ring R, these pairings act R-linearly (or conjugate R-linearly), with values in an R-module.
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Katherine E. Stange (2024) studied this question.
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