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• W3149554512 abstract "Abstract We consider a product $X=E_1times cdots times E_d$ of elliptic curves over a finite extension $K$ of ${mathbb{Q}}_p$ with a combination of good or split multiplicative reduction. We assume that at most one of the elliptic curves has supersingular reduction. Under these assumptions, we prove that the Albanese kernel of $X$ is the direct sum of a finite group and a divisible group, extending work by Raskind and Spiess to cases that include supersingular phenomena. Our method involves studying the kernel of the cycle map $CH_0(X)/p^nrightarrow H^{2d}_{acute{textrm{e}}textrm{t}}(X, mu _{p^n}^{otimes d})$. We give specific criteria that guarantee this map is injective for every $ngeq 1$. When all curves have good ordinary reduction, we show that it suffices to extend to a specific finite extension $L$ of $K$ for these criteria to be satisfied. This extends previous work by Yamazaki and Hiranouchi." @default.
• W3149554512 created "2021-04-13" @default.
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• W3149554512 date "2021-03-31" @default.
• W3149554512 modified "2023-09-26" @default.
• W3149554512 title "Zero Cycles on a Product of Elliptic Curves Over a <i>p</i>-adic Field" @default.
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• W3149554512 doi "https://doi.org/10.1093/imrn/rnab020" @default.
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