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Algebra 3 : homological algebra and its applications / / Ramji Lal
| Algebra 3 : homological algebra and its applications / / Ramji Lal |
| Autore | Lal Ramji |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (310 pages) |
| Disciplina | 512.55 |
| Collana | Infosys Science Foundation series |
| Soggetto topico |
Algebra, Homological
Àlgebra homològica |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 981-336-326-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Intro -- Preface -- Contents -- About the Author -- Notations -- 1 Homological Algebra 1 -- 1.1 Categories and Functors -- 1.2 Abelian Categories -- 1.3 Category of Chain Complexes and Homology -- 1.4 Extensions and the Functor EXT -- 2 Homological Algebra 2, Derived Functors -- 2.1 Resolutions and Extensions -- 2.2 Tensor and Tor Functors -- 2.3 Abstract Theory of Derived Functors -- 2.4 Kunneth Formula -- 2.5 Spectral Sequences -- 3 Homological Algebra 3: Examples and Applications -- 3.1 Polyhedrons and Simplicial Homology -- 3.2 Applications -- 3.3 Co-homology of Groups -- 3.4 Calculus and Co-homology -- 4 Sheaf Co-homology and Its Applications -- 4.1 Presheaves and Sheaves -- 4.2 Sheaf Co-homology and ech Co-homology -- 4.3 Algebraic Varieties -- 4.4 Schemes -- 4.5 Weil Conjectures and l-adic Co-homology -- Appendix Bibliography -- -- Index. |
| Record Nr. | UNISA-996466565903316 |
Lal Ramji
|
||
| Singapore : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Algebra 3 : homological algebra and its applications / / Ramji Lal
| Algebra 3 : homological algebra and its applications / / Ramji Lal |
| Autore | Lal Ramji |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (310 pages) |
| Disciplina | 512.55 |
| Collana | Infosys Science Foundation series |
| Soggetto topico |
Algebra, Homological
Àlgebra homològica |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 981-336-326-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Intro -- Preface -- Contents -- About the Author -- Notations -- 1 Homological Algebra 1 -- 1.1 Categories and Functors -- 1.2 Abelian Categories -- 1.3 Category of Chain Complexes and Homology -- 1.4 Extensions and the Functor EXT -- 2 Homological Algebra 2, Derived Functors -- 2.1 Resolutions and Extensions -- 2.2 Tensor and Tor Functors -- 2.3 Abstract Theory of Derived Functors -- 2.4 Kunneth Formula -- 2.5 Spectral Sequences -- 3 Homological Algebra 3: Examples and Applications -- 3.1 Polyhedrons and Simplicial Homology -- 3.2 Applications -- 3.3 Co-homology of Groups -- 3.4 Calculus and Co-homology -- 4 Sheaf Co-homology and Its Applications -- 4.1 Presheaves and Sheaves -- 4.2 Sheaf Co-homology and ech Co-homology -- 4.3 Algebraic Varieties -- 4.4 Schemes -- 4.5 Weil Conjectures and l-adic Co-homology -- Appendix Bibliography -- -- Index. |
| Record Nr. | UNINA-9910483882903321 |
|
Lal Ramji
|
||
| Singapore : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Determinants, Gröbner bases and cohomology / / Winfried Bruns [and three others]
| Determinants, Gröbner bases and cohomology / / Winfried Bruns [and three others] |
| Autore | Bruns Winfried |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (514 pages) |
| Disciplina | 512.55 |
| Collana | Springer monographs in mathematics |
| Soggetto topico |
Algebra, Homological
Algebraic geometry Commutative algebra Àlgebra homològica Geometria algebraica Àlgebra commutativa |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-05480-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Gröbner Bases, Initial Ideals and Initial Algebras -- 1.1 Monomial Orders -- 1.2 Gröbner Bases -- 1.3 Sagbi Bases -- 1.4 Initial Subspaces and Gradings -- 1.5 Initial Subspaces for Weights. Homogenization -- 1.6 Deformation to the Initial Object -- 2 More on Gröbner Deformations -- 2.1 Minimal and Associated Primes -- 2.2 Connectedness -- 2.3 Optimal Gröbner Deformations -- 2.4 Square-Free Gröbner Deformations -- 3 Determinantal Ideals and the Straightening Law -- 3.1 Minors and Determinantal Ideals -- 3.2 Standard Bitableaux and the Straightening Law -- 3.3 Refinement of the Straightening Law -- 3.4 Determinantal Rings -- 3.5 Powers and Products of Determinantal Ideals -- 3.6 Representation Theory -- 4 Gröbner Bases of Determinantal Ideals -- 4.1 An Instructive Case: the Ideal of 2-Minors -- 4.2 The Robinson-Schensted-Knuth Correspondence -- 4.3 RSK and Gröbner Bases of Ideals -- 4.4 Cohen-Macaulayness and Hilbert Series of Determinantal Rings -- 4.5 Gröbner Bases via Secants -- 4.6 Multigraded Structures and the Multidegree -- 5 Universal Gröbner Bases -- 5.1 Universal Gröbner Bases -- 5.2 Universal Gröbner Bases for Maximal Minors -- 5.3 Universal Gröbner Bases for 2-Minors -- 6 Algebras Defined by Minors -- 6.1 A Recap of Toric Algebra -- 6.2 Algebras Defined by Maximal Minors -- 6.3 Rees Algebras of Determinantal Ideals -- 6.4 The Algebra of Minors -- 6.5 Algebraic Relations between Minors -- 6.6 Exterior Powers of Linear Maps -- 6.7 Sagbi Deformations of Determinantal Rings -- 7 F-singularities of Determinantal Rings -- 7.1 F-purity -- 7.2 F-regularity -- 7.3 F-rationality and Gröbner Deformations -- 7.4 Equivariant Deformations -- 7.5 F-pure Thresholds -- 8 Castelnuovo-Mumford Regularity -- 8.1 Castelnuovo-Mumford Regularity over General Base Rings.
8.2 Castelnuovo-Mumford Regularity and Multigraded Structures -- 8.3 Vanishing over Nonstandard Multigraded Rings -- 8.4 Regularity of Powers and Products of Ideals -- 8.5 Linear Powers and Linear Products -- 8.6 A Family of Determinantal Ideals with Linear Products -- 8.7 Maximal Minors of Matrices of Linear Forms and Linear Powers -- 9 Grassmannians, Flag Varieties, Schur Functors and Cohomology -- 9.1 Fundamental Multilinear Algebra Constructions -- 9.2 Affine and Projective Bundles, Grassmannians, Flag Varieties -- 9.3 Basic Calculus with Direct Images -- 9.4 The Kempf Vanishing Theorem -- 9.5 Characteristic-Free Vanishing for some Nondominant Weights -- 9.6 A Sharp Characteristic-Free Vanishing on Projective Bundles -- 9.7 Algebraic Groups and Representations -- 9.8 Schur Functors -- 9.9 Grothendieck Duality -- 9.10 Cohomology Vanishing on Grassmannians -- 10 Asymptotic Regularity for Symbolic Powers of Determinantal Ideals -- 10.1 Quotients of Ideals Defined by Shape -- 10.2 Filtrations Associated with Ideals Defined by Shape -- 10.3 An algorithm to Compute Z(Σ) -- 10.4 The Filtration for Symbolic Powers of Determinantal Ideals -- 10.5 Sheaves Defined by Shape and Their Quotients -- 10.6 A Geometric Realization of the Modules J(σ)l -- 10.7 Regularity of Symbolic Powers of Determinantal Ideals -- 10.8 Some Geometric Properties of Determinantal Varieties -- 11 Cohomology and Regularity in Characteristic Zero -- 11.1 The Borel-Weil-Bott Theorem -- 11.2 The Optimality of Theorem 9.5.1摥映數爠eflinkthm:charspsfreespsvanishing9.5.19 -- 11.3 Borel-Weil-Bott on Grassmannians -- 11.4 Effective Vanishing of Cohomology in Characteristic Zero -- 11.5 Cauchy's Formula Revisited -- 11.6 Explicit Description of `3́9`42`"̇613A``45`47`"603AExt Modules for J(σ)l -- 11.7 `3́9`42`"̇613A``45`47`"603AExt Modules for Symbolic Powers. 11.8 The Basics on `3́9`42`"̇613A``45`47`"603AGL-Invariant Ideals -- 11.9 `3́9`42`"̇613A``45`47`"603AExt Modules for `3́9`42`"̇613A``45`47`"603AGL-Invariant Ideals -- 11.10 Local Cohomology with Determinantal Support -- 11.11 Syzygies of `3́9`42`"̇613A``45`47`"603AGL-Invariant Ideals -- Appendix List of Symbols -- References -- -- Index. |
| Record Nr. | UNINA-9910633915903321 |
|
Bruns Winfried
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Determinants, Gröbner bases and cohomology / / Winfried Bruns [and three others]
| Determinants, Gröbner bases and cohomology / / Winfried Bruns [and three others] |
| Autore | Bruns Winfried |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (514 pages) |
| Disciplina | 512.55 |
| Collana | Springer monographs in mathematics |
| Soggetto topico |
Algebra, Homological
Algebraic geometry Commutative algebra Àlgebra homològica Geometria algebraica Àlgebra commutativa |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-05480-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Gröbner Bases, Initial Ideals and Initial Algebras -- 1.1 Monomial Orders -- 1.2 Gröbner Bases -- 1.3 Sagbi Bases -- 1.4 Initial Subspaces and Gradings -- 1.5 Initial Subspaces for Weights. Homogenization -- 1.6 Deformation to the Initial Object -- 2 More on Gröbner Deformations -- 2.1 Minimal and Associated Primes -- 2.2 Connectedness -- 2.3 Optimal Gröbner Deformations -- 2.4 Square-Free Gröbner Deformations -- 3 Determinantal Ideals and the Straightening Law -- 3.1 Minors and Determinantal Ideals -- 3.2 Standard Bitableaux and the Straightening Law -- 3.3 Refinement of the Straightening Law -- 3.4 Determinantal Rings -- 3.5 Powers and Products of Determinantal Ideals -- 3.6 Representation Theory -- 4 Gröbner Bases of Determinantal Ideals -- 4.1 An Instructive Case: the Ideal of 2-Minors -- 4.2 The Robinson-Schensted-Knuth Correspondence -- 4.3 RSK and Gröbner Bases of Ideals -- 4.4 Cohen-Macaulayness and Hilbert Series of Determinantal Rings -- 4.5 Gröbner Bases via Secants -- 4.6 Multigraded Structures and the Multidegree -- 5 Universal Gröbner Bases -- 5.1 Universal Gröbner Bases -- 5.2 Universal Gröbner Bases for Maximal Minors -- 5.3 Universal Gröbner Bases for 2-Minors -- 6 Algebras Defined by Minors -- 6.1 A Recap of Toric Algebra -- 6.2 Algebras Defined by Maximal Minors -- 6.3 Rees Algebras of Determinantal Ideals -- 6.4 The Algebra of Minors -- 6.5 Algebraic Relations between Minors -- 6.6 Exterior Powers of Linear Maps -- 6.7 Sagbi Deformations of Determinantal Rings -- 7 F-singularities of Determinantal Rings -- 7.1 F-purity -- 7.2 F-regularity -- 7.3 F-rationality and Gröbner Deformations -- 7.4 Equivariant Deformations -- 7.5 F-pure Thresholds -- 8 Castelnuovo-Mumford Regularity -- 8.1 Castelnuovo-Mumford Regularity over General Base Rings.
8.2 Castelnuovo-Mumford Regularity and Multigraded Structures -- 8.3 Vanishing over Nonstandard Multigraded Rings -- 8.4 Regularity of Powers and Products of Ideals -- 8.5 Linear Powers and Linear Products -- 8.6 A Family of Determinantal Ideals with Linear Products -- 8.7 Maximal Minors of Matrices of Linear Forms and Linear Powers -- 9 Grassmannians, Flag Varieties, Schur Functors and Cohomology -- 9.1 Fundamental Multilinear Algebra Constructions -- 9.2 Affine and Projective Bundles, Grassmannians, Flag Varieties -- 9.3 Basic Calculus with Direct Images -- 9.4 The Kempf Vanishing Theorem -- 9.5 Characteristic-Free Vanishing for some Nondominant Weights -- 9.6 A Sharp Characteristic-Free Vanishing on Projective Bundles -- 9.7 Algebraic Groups and Representations -- 9.8 Schur Functors -- 9.9 Grothendieck Duality -- 9.10 Cohomology Vanishing on Grassmannians -- 10 Asymptotic Regularity for Symbolic Powers of Determinantal Ideals -- 10.1 Quotients of Ideals Defined by Shape -- 10.2 Filtrations Associated with Ideals Defined by Shape -- 10.3 An algorithm to Compute Z(Σ) -- 10.4 The Filtration for Symbolic Powers of Determinantal Ideals -- 10.5 Sheaves Defined by Shape and Their Quotients -- 10.6 A Geometric Realization of the Modules J(σ)l -- 10.7 Regularity of Symbolic Powers of Determinantal Ideals -- 10.8 Some Geometric Properties of Determinantal Varieties -- 11 Cohomology and Regularity in Characteristic Zero -- 11.1 The Borel-Weil-Bott Theorem -- 11.2 The Optimality of Theorem 9.5.1摥映數爠eflinkthm:charspsfreespsvanishing9.5.19 -- 11.3 Borel-Weil-Bott on Grassmannians -- 11.4 Effective Vanishing of Cohomology in Characteristic Zero -- 11.5 Cauchy's Formula Revisited -- 11.6 Explicit Description of `3́9`42`"̇613A``45`47`"603AExt Modules for J(σ)l -- 11.7 `3́9`42`"̇613A``45`47`"603AExt Modules for Symbolic Powers. 11.8 The Basics on `3́9`42`"̇613A``45`47`"603AGL-Invariant Ideals -- 11.9 `3́9`42`"̇613A``45`47`"603AExt Modules for `3́9`42`"̇613A``45`47`"603AGL-Invariant Ideals -- 11.10 Local Cohomology with Determinantal Support -- 11.11 Syzygies of `3́9`42`"̇613A``45`47`"603AGL-Invariant Ideals -- Appendix List of Symbols -- References -- -- Index. |
| Record Nr. | UNISA-996503552303316 |
|
Bruns Winfried
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I [[electronic resource] /] / by Simon Lentner, Svea Nora Mierach, Christoph Schweigert, Yorck Sommerhäuser
| Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups I [[electronic resource] /] / by Simon Lentner, Svea Nora Mierach, Christoph Schweigert, Yorck Sommerhäuser |
| Autore | Lentner Simon |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (76 pages) |
| Disciplina | 530.15423 |
| Altri autori (Persone) |
MierachSvea Nora
SchweigertChristoph SommerhäuserYorck |
| Collana | SpringerBriefs in Mathematical Physics |
| Soggetto topico |
Mathematical physics
Algebraic topology Algebra, Homological Mathematical Physics Algebraic Topology Category Theory, Homological Algebra Àlgebra homològica Àlgebra tensorial Aplicacions (Matemàtica) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 981-19-4645-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Mapping class groups -- Tensor categories -- Derived functors. |
| Record Nr. | UNINA-9910736002203321 |
|
Lentner Simon
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| Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Homotopical topology / / by Anatoly Fomenko, Dmitry Fuchs
| Homotopical topology / / by Anatoly Fomenko, Dmitry Fuchs |
| Autore | Fomenko Anatoly |
| Edizione | [Second edition] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing, [2016] |
| Descrizione fisica | 1 online resource (XI, 627 p. 210 illus.) |
| Disciplina | 512.55 |
| Collana | Graduate Texts in Mathematics |
| Soggetto topico |
Topologia algebraica
Àlgebra homològica Category theory (Mathematics) Homological algebra K-theory Algebraic topology Category Theory, Homological Algebra K-Theory Algebraic Topology |
| ISBN | 3-319-23488-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- Homotopy -- Homology -- Spectral Sequences of Fibrations -- Cohomology Operations -- The Adams Spectral Sequence -- K-Theory and Other Extraordinary Cohomology Theories. |
| Record Nr. | UNINA-9910254096503321 |
|
Fomenko Anatoly
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| Cham : , : Springer International Publishing, [2016] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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