Presenting the 1st systematic remedy of the habit of Néron versions below ramified base swap, this publication could be learn as an advent to varied sophisticated invariants and buildings regarding Néron types of semi-abelian types, influenced by means of concrete examine difficulties and complemented with specific examples.
Néron versions of abelian and semi-abelian kinds became an integral software in algebraic and mathematics geometry due to the fact Néron brought them in his seminal 1964 paper. functions diversity from the speculation of heights in Diophantine geometry to Hodge theory.
We concentration particularly on Néron part teams, Edixhoven’s filtration and the bottom swap conductor of Chai and Yu, and we learn those invariants utilizing numerous thoughts akin to types of curves, sheaves on Grothendieck websites and non-archimedean uniformization. We then follow our effects to the examine of motivic zeta capabilities of abelian forms. the ultimate bankruptcy incorporates a record of not easy open questions. This e-book is aimed in the direction of researchers with a history in algebraic and mathematics geometry.
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