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Title: Geometric generalizations of the square sieve, with an application to cyclic covers
Abstract

We formulate a general problem: Given projective schemes and over a global fieldKand aK‐morphism η from to of finite degree, how many points in of height at mostBhave a pre‐image under η in ? This problem is inspired by a well‐known conjecture of Serre on quantitative upper bounds for the number of points of bounded height on an irreducible projective variety defined over a number field. We give a nontrivial answer to the general problem when and is a prime degree cyclic cover of . Our tool is a new geometric sieve, which generalizes the polynomial sieve to a geometric setting over global function fields.

 
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Award ID(s):
2002716 1652173 2200470
PAR ID:
10401150
Author(s) / Creator(s):
 ;  ;  ;  
Publisher / Repository:
Oxford University Press (OUP)
Date Published:
Journal Name:
Mathematika
Volume:
69
Issue:
1
ISSN:
0025-5793
Page Range / eLocation ID:
p. 106-154
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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