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Award ID contains: 2002716

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  1. ; ; ; (, Mathematika)
    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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  2. ; ; (, Journal of the European Mathematical Society)
    Full Text Available 
  3. (, Panoramas et synthèses Société mathématique de France)
    Bassa, Alp; Lorenzo_Garcia, Elisa; Ritzenthaler, Christophe (Ed.)
    Accepted Manuscript Full Text Available