De Rham Cohomology of Differential Modules on Algebraic Varieties
(Sprache: Englisch)
"...A nice feature of the book [is] that at various points the authors provide examples, or rather counterexamples, that clearly show what can go wrong...This is a nicely-written book [that] studies algebraic differential modules in several variables."
--Mathematical Reviews
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"...A nice feature of the book [is] that at various points the authors provide examples, or rather counterexamples, that clearly show what can go wrong...This is a nicely-written book [that] studies algebraic differential modules in several variables."
--Mathematical Reviews
Inhaltsverzeichnis zu „De Rham Cohomology of Differential Modules on Algebraic Varieties “
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.
Bibliographische Angaben
- Autoren: Yves André , Francesco Baldassarri
- 2001, 214 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 3764363487
- ISBN-13: 9783764363482
- Erscheinungsdatum: 01.12.2000
Sprache:
Englisch
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