Johannes Nicaise's Books

Motivic Integration

By: Antoine Chambert-Loir,Johannes Nicaise,Julien Sebag

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Motivic Integration

By: Antoine Chambert-Loir,Johannes Nicaise,Julien Sebag

This monograph focuses on the geometric theory of motivic integration, which takes its values in the Grothendieck ring of varieties. This theory is rooted in a groundbreaking idea of Kontsevich and was further developed by Denef & Loeser and Sebag. It is presented in the context of formal schemes over a discrete valuation ring, without any restriction on the residue characteristic. The text first discusses the main features of the Grothendieck ring of varieties, arc schemes, and Greenberg schemes. It then moves on to motivic integration and its applications to birational geometry and non-Archimedean geometry. Also included in the work is a prologue on p-adic analytic manifolds, which served as a model for motivic integration. With its extensive discussion of preliminaries and applications, this book is an ideal resource for graduate students of algebraic geometry and researchers of motivic integration. It will also serve as a motivation for more recent and sophisticated theories that have been developed since.

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541

Publisher

Springer

Published Date

ISBN 10

149397887X

ISBN 13

9781493978878

Néron Models and Base Change

By: Lars Halvard Halle,Johannes Nicaise

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Néron Models and Base Change

By: Lars Halvard Halle,Johannes Nicaise

Presenting the first systematic treatment of the behavior of Néron models under ramified base change, this book can be read as an introduction to various subtle invariants and constructions related to Néron models of semi-abelian varieties, motivated by concrete research problems and complemented with explicit examples. Néron models of abelian and semi-abelian varieties have become an indispensable tool in algebraic and arithmetic geometry since Néron introduced them in his seminal 1964 paper. Applications range from the theory of heights in Diophantine geometry to Hodge theory. We focus specifically on Néron 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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Page Count

154

Publisher

Springer

Published Date

ISBN 10

3319266381

ISBN 13

9783319266381

Motivic Integration

By: Antoine Chambert-Loir,Johannes Nicaise,Julien Sebag

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Motivic Integration

By: Antoine Chambert-Loir,Johannes Nicaise,Julien Sebag

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N/A

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Solve jigsaw puzzle

Age

Page Count

541

Publisher

Springer

Published Date

ISBN 10

149397887X

ISBN 13

9781493978878

Néron Models and Base Change

By: Lars Halvard Halle,Johannes Nicaise

Write a review Read reviews Take a Quiz Solve Book Puzzle

Néron Models and Base Change

By: Lars Halvard Halle,Johannes Nicaise

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

154

Publisher

Springer

Published Date

ISBN 10

3319266381

ISBN 13

9783319266381

Book's by Johannes Nicaise

Motivic Integration

Motivic Integration

Néron Models and Base Change

Néron Models and Base Change

Motivic Integration

Motivic Integration

Néron Models and Base Change

Néron Models and Base Change

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