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De Rham Cohomology of Differential Modules on Algebraic Varieties [[electronic resource] /] / by Yves André, Francesco Baldassarri, Maurizio Cailotto
| De Rham Cohomology of Differential Modules on Algebraic Varieties [[electronic resource] /] / by Yves André, Francesco Baldassarri, Maurizio Cailotto |
| Autore | André Yves |
| Edizione | [2nd ed. 2020.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2020 |
| Descrizione fisica | 1 online resource (XIV, 241 p.) |
| Disciplina | 514.23 |
| Collana | Progress in Mathematics |
| Soggetto topico |
Algebraic geometry
Functions of complex variables Commutative algebra Commutative rings Algebraic Geometry Several Complex Variables and Analytic Spaces Commutative Rings and Algebras |
| ISBN | 3-030-39719-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Regularity in several variables -- §1 Geometric models of divisorially valued function fields -- §2 Logarithmic differential operators -- §3 Connections regular along a divisor -- §4 Extensions with logarithmic poles -- §5 Regular connections: the global case -- §6 Exponents -- Appendix A: A letter of Ph. Robba (Nov. 2, 1984) -- Appendix B: Models and log schemes -- 2 Irregularity in several variables -- §1 Spectral norms -- §2 The generalized Poincaré-Katz rank of irregularity -- §3 Some consequences of the Turrittin-Levelt-Hukuhara theorem -- §4 Newton polygons -- §5 Stratification of the singular locus by Newton polygons -- §6 Formal decomposition of an integrable connection at a singular divisor -- §7 Cyclic vectors, indicial polynomials and tubular neighborhoods -- 3 Direct images (the Gauss-Manin connection) -- §1 Elementary fibrations -- §2 Review of connections and De Rham cohomology -- §3 Dévissage -- §4 Generic finiteness of direct images -- §5 Generic base change for direct images -- §6 Coherence of the cokernel of a regular connection -- §7 Regularity and exponents of the cokernel of a regular connection -- §8 Proof of the main theorems: finiteness, regularity, monodromy, base change (in the regular case) -- Appendix C: Berthelot’s comparison theorem on OXDX-linear duals -- Appendix D: Introduction to Dwork’s algebraic dual theory -- 4 Complex and p-adic comparison theorems -- §1 Review of analytic connections and De Rham cohomology -- §2 Abstract comparison criteria -- §3 Comparison theorem for algebraic vs.complex-analytic cohomology -- §4 Comparison theorem for algebraic vs. rigid-analytic cohomology (regular coefficients) -- §5 Rigid-analytic comparison theorem in relative dimension one -- §6 Comparison theorem for algebraic vs. rigid-analytic cohomology (irregular coefficients) -- §7 The relative non-archimedean Turrittin theorem -- Appendix E: Riemann’s “existence theorem” in higher dimension, an elementary approach -- References. |
| Record Nr. | UNINA-9910482961503321 |
André Yves
|
||
| Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
De Rham Cohomology of Differential Modules on Algebraic Varieties [[electronic resource] /] / by Yves André, Francesco Baldassarri, Maurizio Cailotto
| De Rham Cohomology of Differential Modules on Algebraic Varieties [[electronic resource] /] / by Yves André, Francesco Baldassarri, Maurizio Cailotto |
| Autore | André Yves |
| Edizione | [2nd ed. 2020.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2020 |
| Descrizione fisica | 1 online resource (XIV, 241 p.) |
| Disciplina | 514.23 |
| Collana | Progress in Mathematics |
| Soggetto topico |
Algebraic geometry
Functions of complex variables Commutative algebra Commutative rings Algebraic Geometry Several Complex Variables and Analytic Spaces Commutative Rings and Algebras |
| ISBN | 3-030-39719-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Regularity in several variables -- §1 Geometric models of divisorially valued function fields -- §2 Logarithmic differential operators -- §3 Connections regular along a divisor -- §4 Extensions with logarithmic poles -- §5 Regular connections: the global case -- §6 Exponents -- Appendix A: A letter of Ph. Robba (Nov. 2, 1984) -- Appendix B: Models and log schemes -- 2 Irregularity in several variables -- §1 Spectral norms -- §2 The generalized Poincaré-Katz rank of irregularity -- §3 Some consequences of the Turrittin-Levelt-Hukuhara theorem -- §4 Newton polygons -- §5 Stratification of the singular locus by Newton polygons -- §6 Formal decomposition of an integrable connection at a singular divisor -- §7 Cyclic vectors, indicial polynomials and tubular neighborhoods -- 3 Direct images (the Gauss-Manin connection) -- §1 Elementary fibrations -- §2 Review of connections and De Rham cohomology -- §3 Dévissage -- §4 Generic finiteness of direct images -- §5 Generic base change for direct images -- §6 Coherence of the cokernel of a regular connection -- §7 Regularity and exponents of the cokernel of a regular connection -- §8 Proof of the main theorems: finiteness, regularity, monodromy, base change (in the regular case) -- Appendix C: Berthelot’s comparison theorem on OXDX-linear duals -- Appendix D: Introduction to Dwork’s algebraic dual theory -- 4 Complex and p-adic comparison theorems -- §1 Review of analytic connections and De Rham cohomology -- §2 Abstract comparison criteria -- §3 Comparison theorem for algebraic vs.complex-analytic cohomology -- §4 Comparison theorem for algebraic vs. rigid-analytic cohomology (regular coefficients) -- §5 Rigid-analytic comparison theorem in relative dimension one -- §6 Comparison theorem for algebraic vs. rigid-analytic cohomology (irregular coefficients) -- §7 The relative non-archimedean Turrittin theorem -- Appendix E: Riemann’s “existence theorem” in higher dimension, an elementary approach -- References. |
| Record Nr. | UNISA-996418271903316 |
|
André Yves
|
||
| Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||