On the de Rham and $p$-adic realizations of the elliptic polylogarithm for CM elliptic curves
نویسندگان
چکیده
منابع مشابه
ON THE DE RHAM AND p-ADIC REALIZATIONS OF THE ELLIPTIC POLYLOGARITHM FOR CM ELLIPTIC CURVES
In this paper, we give an explicit description of the de Rham and p-adic polylogarithms for elliptic curves using the Kronecker theta function. We prove in particular that when the elliptic curve has complex multiplication and good reduction at p, then the specializations to torsion points of the p-adic elliptic polylogarithm are related to p-adic Eisenstein-Kronecker numbers, proving a p-adic ...
متن کاملON THE REAL HODGE AND p-ADIC REALIZATIONS OF THE ELLIPTIC POLYLOGARITHM FOR CM ELLIPTIC CURVES
In this paper, we give an explicit description of the complex and p-adic polylogarithms for elliptic curves using the Kronecker theta function. We prove in particular that when the elliptic curve has complex multiplication and good reduction at p, then the specializations to torsion points of the p-adic elliptic polylogarithm are related to p-adic Eisenstein-Kronecker numbers, proving a p-adic ...
متن کاملRealizations of the Elliptic Polylogarithm for CM elliptic curves
In these notes, we give an overview of our paper [BKT] which gives an explicit description of the de Rham and p-adic realizations of the elliptic polylogarithm, for a general elliptic curve defined over a subfield of C in the de Rham case and for a CM elliptic curve defined over its field of complex multiplication and with good reduction at the primes above p ≥ 5 in the p-adic case. As explaine...
متن کاملp-ADIC EISENSTEIN-KRONECKER FUNCTIONS AND THE ELLIPTIC POLYLOGARITHM FOR CM ELLIPTIC CURVES
In this paper, we construct p-adic analogues of the Kronecker double series, which we call the Eisenstein-Kronecker series, as Coleman functions on an elliptic curve with complex multiplication. We then show that the periods of the specialization of the p-adic elliptic polylogarithm sheaf to arbitrary non-zero points of the elliptic curve may be expressed using these functions.
متن کاملON THE p-ADIC REALIZATION OF ELLIPTIC POLYLOGARITHMS FOR CM-ELLIPTIC CURVES
Let E be a CM-elliptic curve over Q with good ordinary reduction at a prime p ≥ 5. The purpose of this paper is to construct the p-adic elliptic polylogarithm of E, following the method of A. Beı̆linson and A. Levin. Our main result is that the specializations of this object at torsion points give the special values of the one-variable p-adic L-function of the Grössencharakter associated to E.
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ژورنال
عنوان ژورنال: Annales scientifiques de l'École normale supérieure
سال: 2010
ISSN: 0012-9593,1873-2151
DOI: 10.24033/asens.2119