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Neron models and base change

Halle, Lars Halvard.

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Neron models and base change

Record Type:	Electronic resources : Monograph/item
Title/Author:	Neron models and base change/ by Lars Halvard Halle, Johannes Nicaise.
Author:	Halle, Lars Halvard.
other author:	Nicaise, Johannes.
Published:	Cham :Springer International Publishing : : 2016.,
Description:	x, 151 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Neron models. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-26638-1
ISBN:	9783319266381

Neron models and base change
Halle, Lars Halvard.

Neron models and base change[electronic resource] /by Lars Halvard Halle, Johannes Nicaise. - Cham :Springer International Publishing :2016. - x, 151 p. :ill., digital ;24 cm. - Lecture notes in mathematics,21560075-8434 ;. - Lecture notes in mathematics ;2046..

Presenting the first systematic treatment of the behavior of Neron models under ramified base change, this book can be read as an introduction to various subtle invariants and constructions related to Neron models of semi-abelian varieties, motivated by concrete research problems and complemented with explicit examples. Neron models of abelian and semi-abelian varieties have become an indispensable tool in algebraic and arithmetic geometry since Neron introduced them in his seminal 1964 paper. Applications range from the theory of heights in Diophantine geometry to Hodge theory. We focus specifically on Neron component groups, Edixhoven's filtration and the base change conductor of Chai and Yu, and we study these invariants using various techniques such as models of curves, sheaves on Grothendieck sites and non-archimedean uniformization. We then apply our results to the study of motivic zeta functions of abelian varieties. The final chapter contains a list of challenging open questions. This book is aimed towards researchers with a background in algebraic and arithmetic geometry.

ISBN: 9783319266381

Standard No.: 10.1007/978-3-319-26638-1doiSubjects--Topical Terms:

706136
Neron models.

LC Class. No.: QA564

Dewey Class. No.: 516.35

Neron models and base change
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490 1 $a Lecture notes in mathematics, $x 0075-8434 ; $v 2156
520 $a Presenting the first systematic treatment of the behavior of Neron models under ramified base change, this book can be read as an introduction to various subtle invariants and constructions related to Neron models of semi-abelian varieties, motivated by concrete research problems and complemented with explicit examples. Neron models of abelian and semi-abelian varieties have become an indispensable tool in algebraic and arithmetic geometry since Neron introduced them in his seminal 1964 paper. Applications range from the theory of heights in Diophantine geometry to Hodge theory. We focus specifically on Neron component groups, Edixhoven's filtration and the base change conductor of Chai and Yu, and we study these invariants using various techniques such as models of curves, sheaves on Grothendieck sites and non-archimedean uniformization. We then apply our results to the study of motivic zeta functions of abelian varieties. The final chapter contains a list of challenging open questions. This book is aimed towards researchers with a background in algebraic and arithmetic geometry.
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