0-cycles on singular schemes and class field theory

Amalendu Krishna

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arXiv · 1502.01515

0-cycles on singular schemes and class field theory

Amalendu Krishna

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Abstract

We show that the Chow group of 0-cycles on a singular projective scheme $X$ over a finite field describes the abelian extensions of its function field which are unramified over the regular locus of $X$. As a consequence, we obtain the Bloch-Quillen formula for the Chow group of 0-cycles on such schemes. We deduce simple proofs of results of Kerz-Saito for a class of surfaces without any assumption on ${\rm char}(k)$.

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Amalendu Krishna. 2015-02-05. 0-cycles on singular schemes and class field theory. https://arxiv.org/abs/1502.01515

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