Smoothness of Moduli Space of Stable Torsion-free Sheaves with Fixed Determinant in Mixed Characteristic
Let \( R \) be a complete discrete valuation ring with fraction field of characteristic 0 and algebraically closed residue field of characteristic \( p > 0 \) . Let \( X_{R} \to {\text{Spec}}(R) \) be a smooth projective morphism of relative dimension
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Analytic and Algebraic Geometry
Analytic and Algebraic Geometry
Anilatmaja Aryasomayajula Indranil Biswas Archana S. Morye A.J. Parameswaran •
Editors
Analytic and Algebraic Geometry
123
Editors Anilatmaja Aryasomayajula Department of Mathematics IISER Tirupati Tirupati, Andhra Pradesh India
Archana S. Morye School of Mathematics and Statistics University of Hyderabad Hyderabad, Telangana India
Indranil Biswas School of Mathematics Tata Institute of Fundamental Research Mumbai, Maharashtra India
A.J. Parameswaran School of Mathematics Tata Institute of Fundamental Research Mumbai, Maharashtra India
ISBN 978-981-10-5648-2 (eBook) DOI 10.1007/978-981-10-5648-2 Library of Congress Control Number: 2017946031 This work is a co-publication with Hindustan Book Agency, New Delhi, licensed for sale in all countries in electronic form only. Sold and distributed in print across the world by Hindustan Book Agency, P-19 Green Park Extension, New Delhi 110016, India. ISBN: 978-93-86279-64-4 © Hindustan Book Agency 2017. © Springer Nature Singapore Pte Ltd. 2017 and Hindustan Book Agency 2017 This work is subject to copyright. All rights are reserved by the Publishers, 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 publishers, 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 publishers 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. The publishers remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by Springer Nature The registered company is Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
Preface
For more than ten years, Indranil Biswas and A. J. Parameswaran of Tata Institute of Fundamental Research, Mumbai are organizing an annual international conference on the topics around Analytic and Algebraic Geometry. The first part of the conference is held at the Tata Institute of Fundamental Research and the second part in some other institute. These conferences are primarily intended to facilitate interactions, between mathematicians in India and in other countries, working in related areas. Another
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