Selmer Groups and Torsion Zero Cycles on the Selfproduct of a Semistable Elliptic Curve

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.\par

1991 Mathematics Subject Classification: Primary 14H52; Secondary 19E15, 14F30.\hfill\break Key words and phrases: torsion zero cycles, semistable elliptic curve, multiplicative reduction primes, Selmer group of the symmetric square, Hyodo-Kato cohomology.

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