| Description |
1 online resource (224 p.) |
| Series |
London Mathematical Society Lecture Note Series ; v.490 |
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London Mathematical Society lecture note series.
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| Contents |
Cover -- Series page -- Title page -- Imprints page -- Contents -- 1 Introduction -- 2 Background on C[sup(∞)]-schemes -- 2.1 Introduction to category theory -- 2.2 C[sup(∞)]-rings -- 2.3 Modules and cotangent modules of C[sup(∞)]-rings -- 2.4 Sheaves -- 2.5 C[sup(∞)]-schemes -- 2.6 Complete C[sup(∞)]-rings -- 2.7 Sheaves of O[sub(X)]-modules on C[sup(∞)]-ringed spaces -- 2.8 Sheaves of O[sub(X)]-modules on C[sup(∞)]-schemes -- 2.9 Applications of C[sup(∞)]-rings and C[sup(∞)]-schemes -- 3 Background on manifolds with (g-)corners -- 3.1 Manifolds with corners -- 3.2 Monoids |
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3.3 Manifolds with g-corners -- 3.4 Boundaries, corners, and the corner functor -- 3.5 Tangent bundles and b-tangent bundles -- 3.6 Applications of manifolds with (g-)corners -- 4 (Pre) C[sup(∞)]-rings with corners -- 4.1 Categorical pre C[sup(∞)]-rings with corners -- 4.2 Pre C[sup(∞)]-rings with corners -- 4.3 Adjoints and (co)limits for pre C[sup(∞)]-rings with corners -- 4.4 C[sup(∞)]-rings with corners -- 4.5 Generators, relations, and localization -- 4.6 Local C[sup(∞)]-rings with corners -- 4.7 Special classes of C[sup(∞)]-rings with corners -- 5 C[sup(∞)]-schemes with corners |
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5.1 (Local) C[sup(∞)]-ringed spaces with corners -- 5.2 Special classes of local C[sup(∞)]-ringed spaces with corners -- 5.3 The spectrum functor -- 5.4 C[sup(∞)]-schemes with corners -- 5.5 Semi-complete C[sup(∞)]-rings with corners -- 5.6 Special classes of C[sup(∞)]-schemes with corners -- 5.7 Fibre products of C[sup(∞)]-schemes with corners -- 6 Boundaries, corners, and the corner functor -- 6.1 The corner functor for C[sup(∞)]-ringed spaces with corners -- 6.2 The corner functor for C[sup(∞)]-schemes with corners -- 6.3 The corner functor for firm C[sup(∞)]-schemes with corners |
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6.4 The sheaves of monoids M̌[sup(ex)][sub(C(X))], M̌[sup(in)][sub(C(X))] on C(X) -- 6.5 The boundary ∂X and k-corners C[sub(k)](X) -- 6.6 Fibre products and corner functors -- 6.7 B- and c-transverse fibre products in Man[sup(gc)][sub(in)], C[sup(∞)]Sch[sup(c)][sub(to)] -- 7 Modules, and sheaves of modules -- 7.1 Modules over C[sup(∞)]-rings with corners, (b-)cotangent modules -- 7.2 (B-)cotangent modules for manifolds with (g-)corners -- 7.3 Some computations of b-cotangent modules -- 7.4 B-cotangent modules of pushouts -- 7.5 Sheaves of O[sub(X)]-modules, and (b-)cotangent sheaves |
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7.6 (B-)cotangent sheaves and the corner functor -- 8 Further generalizations and applications -- 8.1 Synthetic Differential Geometry with corners -- 8.2 C[sup(∞)]-stacks with corners -- 8.3 C[sup(∞)]-rings and C[sup(∞)]-schemes with a-corners -- 8.4 Derived manifolds and orbifolds with corners -- References -- Glossary of Notation -- Index |
| Summary |
Crossing the boundary between differential and algebraic geometry in order to study singular spaces, this book introduces 'C∞-schemes with corners' |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Geometry, Algebraic.
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| Form |
Electronic book
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| Author |
Joyce, Dominic D.
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| ISBN |
9781009400206 |
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1009400207 |
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1009400193 |
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9781009400190 |
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