Zero Cycles on a Product of Elliptic Curves Over a p-adic Field

@article{Gazaki2018ZeroCO,
  title={Zero Cycles on a Product of Elliptic Curves Over a p-adic Field},
  author={Evangelia Gazaki and I. Leal},
  journal={arXiv: Number Theory},
  year={2018}
}
We consider a product $X=E_1\times\cdots\times E_d$ 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 give sufficient criteria for the cycle map $CH_0(X)/p^n\rightarrow H^{2d}_{\text{\'{e}t}}(X, \mu_{p^n}^{\otimes d})$ to be injective for every $n\geq 1$. When all curves have good reduction, we show that it… Expand
3 Citations
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