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(Ebook) C∞-Algebraic Geometry with Corners 1st Edition by Kelli Francis Staite, Dominic Joyce ISBN 9781009400190 1009400169

  • SKU: EBN-56522594
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Instant download (eBook) C∞-Algebraic Geometry with Corners (London Mathematical Society Lecture Note, 490) after payment.
Authors:Francis-Staite, Kelli
Pages:222 pages.
Year:2024
Editon:1
Publisher:Cambridge University Press
Language:english
File Size:2.19 MB
Format:pdf
ISBNS:9781009400190, 9781009400169
Categories: Ebooks

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(Ebook) C∞-Algebraic Geometry with Corners 1st Edition by Kelli Francis Staite, Dominic Joyce ISBN 9781009400190 1009400169

(Ebook) C∞-Algebraic Geometry with Corners 1st Edition by Kelli Francis Staite, Dominic Joyce - Ebook PDF Instant Download/Delivery: 9781009400190 ,1009400169
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ISBN 10: 1009400169
ISBN 13: 9781009400190
Author: Kelli Francis Staite, Dominic Joyce

Schemes in algebraic geometry can have singular points, whereas differential geometers typically focus on manifolds which are nonsingular. However, there is a class of schemes, 'C8-schemes', which allow differential geometers to study a huge range of singular spaces, including 'infinitesimals' and infinite-dimensional spaces. These are applied in synthetic differential geometry, and derived differential geometry, the study of 'derived manifolds'. Differential geometers also study manifolds with corners. The cube is a 3-dimensional manifold with corners, with boundary the six square faces. This book introduces 'C8-schemes with corners', singular spaces in differential geometry with good notions of boundary and corners. They can be used to define 'derived manifolds with corners' and 'derived orbifolds with corners'. These have applications to major areas of symplectic geometry involving moduli spaces of J-holomorphic curves. This work will be a welcome source of information and inspiration for graduate students and researchers working in differential or algebraic geometry.

(Ebook) C∞-Algebraic Geometry with Corners 1st Edition Table of contents:

Part I: C∞C^inftyC∞-Algebra and Geometry

  1. C∞C^inftyC∞-Rings

  2. Modules and Cotangent Modules of C∞C^inftyC∞-Rings

  3. Sheaves

  4. C∞C^inftyC∞-Schemes

  5. Complete C∞C^inftyC∞-Rings

  6. Sheaves of OXmathcal{O}_XOX​-Modules on C∞C^inftyC∞-Ringed Spaces

  7. Sheaves of OXmathcal{O}_XOX​-Modules on C∞C^inftyC∞-Schemes

  8. Applications of C∞C^inftyC∞-Rings and C∞C^inftyC∞-Schemes

Part II: Manifolds with Corners and Generalizations

  1. Background on Manifolds with (g-)Corners

  2. Manifolds with Corners

  3. Monoids

  4. Manifolds with g-Corners

  5. Boundaries, Corners, and the Corner Functor

  6. Tangent Bundles and b-Tangent Bundles

  7. Applications of Manifolds with (g-)Corners

Part III: C∞C^inftyC∞-Rings with Corners

  1. (Pre)C∞C^inftyC∞-Rings with Corners

  2. Categorical Pre-C∞C^inftyC∞-Rings with Corners

  3. Pre-C∞C^inftyC∞-Rings with Corners

  4. Adjoints and (Co)limits for Pre-C∞C^inftyC∞-Rings with Corners

  5. C∞C^inftyC∞-Rings with Corners

  6. Generators, Relations, and Localization

  7. Local C∞C^inftyC∞-Rings with Corners

  8. Special Classes of C∞C^inftyC∞-Rings with Corners

Part IV: C∞C^inftyC∞-Schemes with Corners

  1. C∞C^inftyC∞-Schemes with Corners

  2. (Local) C∞C^inftyC∞-Ringed Spaces with Corners

  3. Special Classes of Local C∞C^inftyC∞-Ringed Spaces with Corners

  4. The Spectrum Functor

  5. C∞C^inftyC∞-Schemes with Corners

  6. Semi-Complete C∞C^inftyC∞-Rings with Corners

  7. Special Classes of C∞C^inftyC∞-Schemes with Corners

  8. Fibre Products of C∞C^inftyC∞-Schemes with Corners

Part V: Corner Functors and Sheaves of Monoids

  1. Boundaries, Corners, and the Corner Functor

  2. The Corner Functor for C∞C^inftyC∞-Ringed Spaces with Corners

  3. The Corner Functor for C∞C^inftyC∞-Schemes with Corners

  4. The Corner Functor for Firm C∞C^inftyC∞-Schemes with Corners

  5. The Sheaves of Monoids Mex,Minmathcal{M}_{text{ex}}, mathcal{M}_{text{in}}Mex​,Min​ on C(X)C(X)C(X)

  6. The Boundary ∂Xpartial X∂X and kkk-Corners Ck(X)C^k(X)Ck(X)

  7. Fibre Products and Corner Functors

  8. B- and c-Transverse Fibre Products in Mangctext{Man}^{text{gc}}Mangc, C∞SchctC^infty text{Sch}_{text{ct}}C∞Schct​

Part VI: Modules and Cotangent Sheaves

  1. Modules and Sheaves of Modules

  2. Modules over C∞C^inftyC∞-Rings with Corners, (b-)Cotangent Modules

  3. (B-)Cotangent Modules for Manifolds with (g-)Corners

  4. Some Computations of b-Cotangent Modules

  5. b-Cotangent Modules of Pushouts

  6. Sheaves of OXmathcal{O}_XOX​-Modules and (b-)Cotangent Sheaves

  7. (B-)Cotangent Sheaves and the Corner Functor

Part VII: Advanced Topics and Applications

  1. Further Generalizations and Applications

  2. Synthetic Differential Geometry with Corners

  3. C∞C^inftyC∞-Stacks with Corners

  4. C∞C^inftyC∞-Rings and C∞C^inftyC∞-Schemes with a-Corners

  5. Derived Manifolds and Orbifolds with Corners

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Tags: Kelli Francis Staite, Dominic Joyce, C∞-Algebraic, Corners

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