## 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 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 language | English (US) |
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Pages (from-to) | 123-146 |

Number of pages | 24 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 166 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2019 |