| Sumario: | Let E be a rational elliptic curve and let p be an odd prime of additive reduction. Let K be an imaginary quadratic field and fix a positive integer c prime to the conductor of E. The main goal of the present article is to define an anticyclotomic p-adic L-function L attached to E/K when E/Qp attains semistable reduction over an abelian extension. We prove that L satisfies the expected interpolation properties; namely, we show that if χ is an anticyclotomic character of conductor cpn, then χ(L) is equal (up to explicit constants) to L(E,χ,1) or L′(E,χ,1). © 2018 Académie des sciences
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