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arXiv · 1908.06424

Selmer group associated to the Chow group of certain codimension two cycles

Kalyan Banerjee·Kalyan Chakraborty
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Abstract

Let $X$ be a surface with geometric genus and irregularity zero which is defined over a number field $K$. Let $\mathscr{X}$ denote a smooth spread of $X$ over the spectrum of a Zariski open subset in the spectrum of the ring of integers and $A^2$ stands for the group of algebraically trivial cycles on schemes modulo rational equivalence. If $j^*: A^2(\mathscr{X})\to A^2(X)$ be the flat pull-back corresponding to the embedding $j:X\hookrightarrow \mathscr{X}$ then we prove that $\im(j^*)(K)/A^2(\mathscr{X})(K)$ is a torsion group. Here $\im(j^*)(K)$, $A^2(\mathscr{X})(K)$ stand for the cycles fixed under the action of the absolute Galois group.

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Kalyan Banerjee, Kalyan Chakraborty. 2019-08-18. Selmer group associated to the Chow group of certain codimension two cycles. https://arxiv.org/abs/1908.06424

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