0000000000435379

AUTHOR

Erwan Rousseau

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

2020

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.

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)International Mathematics Research Notices
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