By Lars Halvard Halle, Johannes Nicaise

ISBN-10: 3319266373

ISBN-13: 9783319266374

ISBN-10: 3319266381

ISBN-13: 9783319266381

Presenting the 1st systematic remedy of the habit of Néron types below ramified base switch, this ebook may be learn as an creation to numerous refined invariants and structures on the topic of Néron types of semi-abelian forms, prompted via concrete examine difficulties and complemented with specific examples.

Néron types of abelian and semi-abelian forms became an integral software in algebraic and mathematics geometry on the grounds that Néron brought them in his seminal 1964 paper. purposes diversity from the idea of heights in Diophantine geometry to Hodge concept.

We concentration in particular on Néron part teams, Edixhoven’s filtration and the bottom swap conductor of Chai and Yu, and we research those invariants utilizing a number of suggestions resembling types of curves, sheaves on Grothendieck websites and non-archimedean uniformization. We then follow our effects to the research of motivic zeta features of abelian types. the ultimate bankruptcy encompasses a checklist of tough open questions. This booklet is aimed in the direction of researchers with a historical past in algebraic and mathematics geometry.