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)|
|Number of pages||24|
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|State||Published - Jan 1 2019|