Advertisement

Nonarchimedean and Tropical Geometry

  • Matthew Baker
  • Sam Payne

Part of the Simons Symposia book series (SISY)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Sébastien Boucksom, Charles Favre, Mattias Jonsson
    Pages 31-49
  3. Johannes Nicaise
    Pages 173-194
  4. Dan Abramovich, Qile Chen, Steffen Marcus, Martin Ulirsch, Jonathan Wise
    Pages 287-336
  5. Tyler Foster
    Pages 337-364
  6. Eric Katz
    Pages 435-517
  7. Back Matter
    Pages 519-526

About these proceedings

Introduction

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–Ampère 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.

Keywords

Tropical Geometry Nonarchimedean Analysis algebraic geometry Berkovich Spaces Hodge Theory Huber Theory

Editors and affiliations

  • Matthew Baker
    • 1
  • Sam Payne
    • 2
  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of MathematicsYale UniversityNew HavenUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-30945-3
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-30944-6
  • Online ISBN 978-3-319-30945-3
  • Series Print ISSN 2365-9564
  • Series Online ISSN 2365-9572
  • Buy this book on publisher's site