Appendix C: Basic Algebra
In this appendix we recall some basic algebraic notions. We first study some constructions in the category of modules. The following sections are a short reminder on several multilinear constructions, in particular tensor products and exterior products. W
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Torsten Wedhorn
Manifolds, Sheaves, and Cohomology
Springer Studium Mathematik – Master Series editors M. Aigner, Freie Universität Berlin, Berlin, Germany H. Faßbender, Technische Universität Braunschweig, Braunschweig, Germany B. Gentz, Universität Bielefeld, Bielefeld, Germany D. Grieser, Universität Oldenburg, Oldenburg, Germany P. Gritzmann, Technische Universität München, Garching, Germany J. Kramer, Humboldt-Universität zu Berlin, Berlin, Germany V. Mehrmann, Technische Universität Berlin, Berlin, Germany G. Wüstholz, ETH Zürich, Zürich, Switzerland
The series „Springer Studium Mathematik“ is aimed at students of all areas of mathematics, as well as those studying other subjects involving mathematics, and anyone working in the field of applied mathematics or in teaching. The series is designed for Bachelor’s and Master’s courses in mathematics, and depending on the courses offered by universities, the books can also be made available in English.
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Torsten Wedhorn
Manifolds, Sheaves, and Cohomology
Torsten Wedhorn Technische Universität Darmstadt Darmstadt, Germany
Springer Studium Mathematik – Master ISBN 978-3-658-10632-4 DOI 10.1007/978-3-658-10633-1
ISBN 978-3-658-10633-1 (eBook)
Library of Congress Control Number: 2016947452 Mathematics Subject Classification (2010): 14-0, 18-01 Springer Spektrum © Springer Fachmedien Wiesbaden 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. Editor: Ulrike Schmickler-Hirzebruch Printed on acid-free paper This Springer Spektrum imprint is published by Springer Nature The registered company is Springer Fachmedien Wiesbaden
Preface
The language of geometry has changed drastically in the last decades. New and fundamental ideas such as the language of categories, sheaves, and cohomology are now indispensable in many incarnations of geometry, such as the theory of complex analytic spaces, algebraic geometry, or non-archimedean geometry. This boo
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