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Nonarchimedean and Tropical Geometry

  • Conference proceedings
  • © 2016

Overview

Editors:
  1. Matthew Baker

    1. School of Mathematics, Georgia Institute of Technology, Atlanta, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Sam Payne

    1. Department of Mathematics, Yale University, New Haven, USA

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Simons Symposia (SISY)

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Table of contents (12 papers)

  1. Front Matter

    Pages i-xiv
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  2. Forms and Currents on the Analytification of an Algebraic Variety (After Chambert-Loir and Ducros)

    • Walter Gubler
    Pages 1-30

  3. The Non-Archimedean Monge–Ampère Equation

    • Sébastien Boucksom, Charles Favre, Mattias Jonsson
    Pages 31-49

  4. Convergence Polygons for Connections on Nonarchimedean Curves

    • Kiran S. Kedlaya
    Pages 51-97

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

    • Antoine Ducros
    Pages 99-131

  6. Excluded Homeomorphism Types for Dual Complexes of Surfaces

    • Dustin Cartwright
    Pages 133-144

  7. Analytification and Tropicalization Over Non-archimedean Fields

    • Annette Werner
    Pages 145-171

  8. Berkovich Skeleta and Birational Geometry

    • Johannes Nicaise
    Pages 173-194

  9. Metrization of Differential Pluriforms on Berkovich Analytic Spaces

    • Michael Temkin
    Pages 195-285

  10. Skeletons and Fans of Logarithmic Structures

    • Dan Abramovich, Qile Chen, Steffen Marcus, Martin Ulirsch, Jonathan Wise
    Pages 287-336

  11. Introduction to Adic Tropicalization

    • Tyler Foster
    Pages 337-364

  12. Degeneration of Linear Series from the Tropical Point of View and Applications

    • Matthew Baker, David Jensen
    Pages 365-433

  13. Matroid Theory for Algebraic Geometers

    • Eric Katz
    Pages 435-517

  14. Back Matter

    Pages 519-526
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Keywords

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.

Editors and Affiliations

  • School of Mathematics, Georgia Institute of Technology, Atlanta, USA

    Matthew Baker

  • Department of Mathematics, Yale University, New Haven, USA

    Sam Payne

Bibliographic Information

  • Book Title: Nonarchimedean and Tropical Geometry

  • Editors: Matthew Baker, Sam Payne

  • Series Title: Simons Symposia

  • DOI: https://doi.org/10.1007/978-3-319-30945-3

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Hardcover ISBN: 978-3-319-30944-6Published: 19 August 2016

  • Softcover ISBN: 978-3-319-80924-3Published: 09 June 2018

  • eBook ISBN: 978-3-319-30945-3Published: 18 August 2016

  • Series ISSN: 2365-9564

  • Series E-ISSN: 2365-9572

  • Edition Number: 1

  • Number of Pages: XIV, 526

  • Number of Illustrations: 79 b/w illustrations, 10 illustrations in colour

  • Topics: Algebraic Geometry

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