# 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

Some results about zero-cycles on abelian and semi-abelian varieties

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In this short note we extend some results obtained in \cite{Gazaki2015}. First, we prove that for an abelian variety $A$ with good ordinary reduction over a finite extension of $\mathbb{Q}_p$ with… Expand

Divisibility results for zero-cycles

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Let $X$ be an abelian variety or a product of curves over a finite unramified extension $k$ of $\mathbb{Q}_p$. Suppose that the Albanese variety of $X$ has good reduction. We propose the following… Expand

Rational Equivalences on Products of Elliptic Curves in a Family

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Given a pair of elliptic curves $E_1,E_2$ over a field $k$, we have a natural map $\text{CH}^1(E_1)_0\otimes\text{CH}^1(E_2)_0\to\text{CH}^2(E_1\times E_2)$, and a conjecture due to Beilinson… Expand

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