Nonarchimedean and Tropical Geometry
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 b
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Matthew Baker Sam Payne Editors
Nonarchimedean and Tropical Geometry
Simons Symposia
More information about this series at http://www.springer.com/series/15045
Matthew Baker • Sam Payne Editors
Nonarchimedean and Tropical Geometry
123
Editors Matthew Baker School of Mathematics Georgia Institute of Technology Atlanta, GA, USA
Sam Payne Department of Mathematics Yale University New Haven, CT, USA
ISSN 2365-9564 ISSN 2365-9572 (electronic) Simons Symposia ISBN 978-3-319-30944-6 ISBN 978-3-319-30945-3 (eBook) DOI 10.1007/978-3-319-30945-3 Library of Congress Control Number: 2016942131 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
Preface
1 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. Although the participants were few in number, they brought widely ranging expertise, a high level of energy, and focused engagement. The articles collected here, which include high-level surveys as well as original research, give a fairly accurate portrait of the main themes running through the lectures and the mathematical discussions of these two symposia. Both tropical geometry and nonarchimedean analytic geometry in the sense of Berkovich produce “nice” (e.g., Hausdorff, path connected, locally contractible) topological spaces associated to varieties over valued fields. These topological spaces are the main feature which distinguishes tropical
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