Anticyclotomic p-adic L-functions for elliptic curves at some additive reduction primes Fonctions L p-adiques anti-cyclotomiques pour les courbes elliptiques en des premiers de réduction additive

PACETTI, ARIEL; KOHEN, DANIEL

COMPTES RENDUS MATHEMATIQUE

ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER

Año: 2018 vol. 356 p. 973 - 983

1631-073X

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/Q p 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 cp n , then χ(L) is equal (up to explicit constants) to L(E,χ,1) or L ′ (E,χ,1).