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Algebraic Geometry Over (Record no. 13674)

MARC details
000 -LEADER
fixed length control field 05863nam a22004453i 4500
001 - CONTROL NUMBER
control field EBC5904555
003 - CONTROL NUMBER IDENTIFIER
control field MiAaPQ
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20240724113947.0
006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS
fixed length control field m o d |
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr cnu||||||||
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 240724s2019 xx o ||||0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781470453367
Qualifying information (electronic bk.)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Canceled/invalid ISBN 9781470436452
035 ## - SYSTEM CONTROL NUMBER
System control number (MiAaPQ)EBC5904555
035 ## - SYSTEM CONTROL NUMBER
System control number (Au-PeEL)EBL5904555
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC)1125109159
040 ## - CATALOGING SOURCE
Original cataloging agency MiAaPQ
Language of cataloging eng
Description conventions rda
-- pn
Transcribing agency MiAaPQ
Modifying agency MiAaPQ
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA564 .J69 2019
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Joyce, Dominic.
245 10 - TITLE STATEMENT
Title Algebraic Geometry Over
-- ^{∞}
-- Rings.
250 ## - EDITION STATEMENT
Edition statement 1st ed.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture Providence :
Name of producer, publisher, distributor, manufacturer American Mathematical Society,
Date of production, publication, distribution, manufacture, or copyright notice 2019.
264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Date of production, publication, distribution, manufacture, or copyright notice ©2019.
300 ## - PHYSICAL DESCRIPTION
Extent 1 online resource (152 pages)
336 ## - CONTENT TYPE
Content type term text
Content type code txt
Source rdacontent
337 ## - MEDIA TYPE
Media type term computer
Media type code c
Source rdamedia
338 ## - CARRIER TYPE
Carrier type term online resource
Carrier type code cr
Source rdacarrier
490 1# - SERIES STATEMENT
Series statement Memoirs of the American Mathematical Society Series ;
Volume/sequential designation v.260
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. ^{\iy}-rings -- 2.1. Two definitions of ^{\iy}-ring -- 2.2. ^{\iy}-rings as commutative \R-algebras, and ideals -- 2.3. Local ^{\iy}-rings, and localization -- 2.4. Fair ^{\iy}-rings -- 2.5. Pushouts of ^{\iy}-rings -- 2.6. Flat ideals -- Chapter 3. The ^{\iy}-ring ^{\iy}( ) of a manifold -- Chapter 4. ^{\iy}-ringed spaces and ^{\iy}-schemes -- 4.1. Some basic topology -- 4.2. Sheaves on topological spaces -- 4.3. ^{\iy}-ringed spaces and local ^{\iy}-ringed spaces -- 4.4. The spectrum functor -- 4.5. Affine ^{\iy}-schemes and ^{\iy}-schemes -- 4.6. Complete ^{\iy}-rings -- 4.7. Partitions of unity -- 4.8. A criterion for affine ^{\iy}-schemes -- 4.9. Quotients of ^{\iy}-schemes by finite groups -- Chapter 5. Modules over ^{\iy}-rings and ^{\iy}-schemes -- 5.1. Modules over ^{\iy}-rings -- 5.2. Cotangent modules of ^{\iy}-rings -- 5.3. Sheaves of Ø_{ }-modules on a ^{\iy}-ringed space ( ,Ø_{ }) -- 5.4. Sheaves on affine ^{\iy}-schemes, \MSpec and \Ga -- 5.5. Complete modules over ^{\iy}-rings -- 5.6. Cotangent sheaves of ^{\iy}-schemes -- Chapter 6. ^{\iy}-stacks -- 6.1. ^{\iy}-stacks -- 6.2. Properties of 1-morphisms of ^{\iy}-stacks -- 6.3. Open ^{\iy}-substacks and open covers -- 6.4. The underlying topological space of a ^{\iy}-stack -- 6.5. Gluing ^{\iy}-stacks by equivalences -- Chapter 7. Deligne-Mumford ^{\iy}-stacks -- 7.1. Quotient ^{\iy}-stacks, 1-morphisms, and 2-morphisms -- 7.2. Deligne-Mumford ^{\iy}-stacks -- 7.3. Characterizing Deligne-Mumford ^{\iy}-stacks -- 7.4. Quotient ^{\iy}-stacks, 1- and 2-morphisms as local models for objects, 1- and 2-morphisms in \DMCSta -- 7.5. Effective Deligne-Mumford ^{\iy}-stacks -- 7.6. Orbifolds as Deligne-Mumford ^{\iy}-stacks -- Chapter 8. Sheaves on Deligne-Mumford ^{\iy}-stacks.
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 8.1. Quasicoherent sheaves -- 8.2. Writing sheaves in terms of a groupoid presentation -- 8.3. Pullback of sheaves as a weak 2-functor -- 8.4. Cotangent sheaves of Deligne-Mumford ^{\iy}-stacks -- Chapter 9. Orbifold strata of ^{\iy}-stacks -- 9.1. The definition of orbifold strata \cX^{\Ga},…,\hcX^{\Ga}_{\ci} -- 9.2. Lifting 1- and 2-morphisms to orbifold strata -- 9.3. Orbifold strata of quotient ^{\iy}-stacks [\uX/ ] -- 9.4. Sheaves on orbifold strata -- 9.5. Sheaves on orbifold strata of quotients [\uX/ ] -- 9.6. Cotangent sheaves of orbifold strata -- Appendix A. Background material on stacks -- A.1. Introduction to 2-categories -- A.2. Grothendieck topologies, sites, prestacks, and stacks -- A.3. Descent theory on a site -- A.4. Properties of 1-morphisms -- A.5. Geometric stacks, and stacks associated to groupoids -- Bibliography -- Glossary of Notation -- Index -- Back Cover.
520 ## - SUMMARY, ETC.
Summary, etc. If X is a manifold then the \mathbb R-algebra C^\infty (X) of smooth functions c:X\rightarrow \mathbb R is a C^\infty -ring. That is, for each smooth function f:\mathbb R^n\rightarrow \mathbb R there is an n-fold operation \Phi _f:C^\infty (X)^n\rightarrow C^\infty (X) acting by \Phi _f:(c_1,\ldots ,c_n)\mapsto f(c_1,\ldots ,c_n), and these operations \Phi _f satisfy many natural identities. Thus, C^\infty (X) actually has a far richer structure than the obvious \mathbb R-algebra structure. The author explains the foundations of a version of algebraic geometry in which rings or algebras are replaced by C^\infty -rings. As schemes are the basic objects in algebraic geometry, the new basic objects are C^\infty -schemes, a category of geometric objects which generalize manifolds and whose morphisms generalize smooth maps. The author also studies quasicoherent sheaves on C^\infty -schemes, and C^\infty -stacks, in particular Deligne-Mumford C^\infty-stacks, a 2-category of geometric objects generalizing orbifolds. Many of these ideas are not new: C^\infty-rings and C^\infty -schemes have long been part of synthetic differential geometry. But the author develops them in new directions. In earlier publications, the author used these tools to define d-manifolds and d-orbifolds, "derived" versions of manifolds and orbifolds related to Spivak's "derived manifolds".
588 ## - SOURCE OF DESCRIPTION NOTE
Source of description note Description based on publisher supplied metadata and other sources.
590 ## - LOCAL NOTE (RLIN)
Local note Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Geometry, Algebraic.
655 #4 - INDEX TERM--GENRE/FORM
Genre/form data or focus term Electronic books.
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Print version:
Main entry heading Joyce, Dominic
Title Algebraic Geometry Over
-- ^{∞}
-- Rings
Place, publisher, and date of publication Providence : American Mathematical Society,c2019
International Standard Book Number 9781470436452
797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN)
Corporate name or jurisdiction name as entry element ProQuest (Firm)
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Memoirs of the American Mathematical Society Series
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5904555">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5904555</a>
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