Selmer groups and torsion zero cycles on the selfproduct of a semistable elliptic curve

Abstract

In this paper we extend the finiteness result on the $p$-primary torsion subgroup in the Chow group of zero cycles on the selfproduct of a semistable elliptic curve obtained in joint work with S. Saito to primes $p$ dividing the conductor. On the way we show the finiteness of the Selmer group associated to the symmetric square of the elliptic curve for those primes. The proof uses $p$-adic techniques, in particular the Fontaine-Jannsen conjecture proven by Kato and Tsuji.