Analytic number theory for 0-cycles


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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 factorisation 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.

Original languageEnglish (US)
Pages (from-to)123-146
Number of pages24
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number1
StatePublished - Jan 1 2019

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