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RESEARCH PRODUCT

Albanese Maps and Fundamental Groups of Varieties With Many Rational Points Over Function Fields

Erwan RousseauAriyan Javanpeykar

subject

Fundamental groupPure mathematicsGeneral Mathematics01 natural sciencesSurjective functionMathematics - Algebraic GeometryMathematics::Algebraic Geometry0103 physical sciencesFOS: MathematicsNumber Theory (math.NT)0101 mathematicsAbelian groupAlgebraic Geometry (math.AG)Projective varietyQuotientFunction fieldMathematicsMathematics - Number Theory010102 general mathematics[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG][MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV]Codimension[MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV][MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]010307 mathematical physicsVariety (universal algebra)

description

We investigate properties of the Albanese map and the fundamental group of a complex projective variety with many rational points over some function field, and prove that every linear quotient of the fundamental group of such a variety is virtually abelian, as well as that its Albanese map is surjective, has connected fibres, and has no multiple fibres in codimension one.

yearjournalcountryeditionlanguage
2020-10-07International Mathematics Research Notices
https://doi.org/10.1093/imrn/rnab255