Zero-cycles on Self-product of Modular Curves
نویسنده
چکیده
arising from the localization sequence in algebraic K-theory has a torsion cokernel. Here p runs over a set of primes which satisfy a certain condition explained below. When C is an elliptic curve, all but finite number of primes p satisfy the condition. By using this fact, Langer and Saito give a finiteness result for the torsion subgroup of the Chow group CH(C × C)([LS]). When g = genus(C) > 1 there seems to be infinitely many primes which do not satisfy the condition, so the finiteness result we obtain is about CH2(C×C× specQp) for the primes p which satisfy the condition. A conjecture of Beilinson on the special values of L-function and Tate conjecture tell us that the cokernel of ∂ is torsion with p running over all but finitely many primes. See the remark after Theorem 2.5 in [Lang] for an account of this.
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