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arXiv · 1603.07212

Analytic number theory for 0-cycles

Weiyan Chen
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Abstract

There is a well-known analogy between integers and polynomials over $F_q$, and a vast literature on analytic number theory for polynomials. From a geometric point of view, polynomials are equivalent to effective 0-cycles on the affine line. This leads one to ask: Can the analogy between integers and polynomials be extended to 0-cycles on more general varieties? In this paper we study prime factorization of effective 0-cycles on an arbitrary connected variety $V$ over $F_q$, emphasizing the analogy between integers and 0-cycles. For example, inspired by the works of Granville and Rhoades, we prove that the prime factors of 0-cycles are typically Poisson distributed.

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Weiyan Chen. 2016-12-06. Analytic number theory for 0-cycles. https://doi.org/10.1017/s0305004117000767

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