Simons Symposia

Nonarchimedean and Tropical Geometry

Editors: Baker, Matthew, Payne, Sam (Eds.)

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eBook $129.00
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  • ISBN 978-3-319-30945-3
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Hardcover $169.00
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  • ISBN 978-3-319-30944-6
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About this book

This volume grew out of two Simons Symposia on "Nonarchimedean and tropical geometry" which took place on the island of St. John in April 2013 and in Puerto Rico in February 2015. Each meeting gathered a small group of experts working near the interface between tropical geometry and nonarchimedean analytic spaces for a series of inspiring and provocative lectures on cutting edge research, interspersed with lively discussions and collaborative work in small groups. The articles collected here, which include high-level surveys as well as original research, mirror the main themes of the two Symposia.

Topics covered in this volume include: 

  • Differential forms and currents, and solutions of Monge-Ampere type differential equations on Berkovich spaces and their skeletons; 
  • The homotopy types of nonarchimedean analytifications;
  • The existence of "faithful tropicalizations" which encode the topology and geometry of analytifications;
  • Relations between nonarchimedean analytic spaces and algebraic geometry, including logarithmic schemes, birational geometry, and the geometry of algebraic curves;
  • Extended notions of tropical varieties which relate to Huber's theory of adic spaces analogously to the way that usual tropical varieties relate to Berkovich spaces; and 
  • Relations between nonarchimedean geometry and combinatorics, including deep and fascinating connections between matroid theory, tropical geometry, and Hodge theory.

Table of contents (12 chapters)

  • Forms and Currents on the Analytification of an Algebraic Variety (After Chambert-Loir and Ducros)

    Gubler, Walter

    Pages 1-30

  • The Non-Archimedean Monge–Ampère Equation

    Boucksom, Sébastien (et al.)

    Pages 31-49

  • Convergence Polygons for Connections on Nonarchimedean Curves

    Kedlaya, Kiran S.

    Pages 51-97

  • About Hrushovski and Loeser’s Work on the Homotopy Type of Berkovich Spaces

    Ducros, Antoine

    Pages 99-131

  • Excluded Homeomorphism Types for Dual Complexes of Surfaces

    Cartwright, Dustin

    Pages 133-144

Buy this book

eBook $129.00
price for USA (gross)
  • ISBN 978-3-319-30945-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.00
price for USA
  • ISBN 978-3-319-30944-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Nonarchimedean and Tropical Geometry
Editors
  • Matthew Baker
  • Sam Payne
Series Title
Simons Symposia
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-30945-3
DOI
10.1007/978-3-319-30945-3
Hardcover ISBN
978-3-319-30944-6
Series ISSN
2365-9564
Edition Number
1
Number of Pages
XIV, 526
Number of Illustrations and Tables
79 b/w illustrations, 10 illustrations in colour
Topics