De Rham Cohomology of Differential Modules on Algebraic Varieties

Andre, Yves; Baldassarri, Francesco

ISBN 10: 3764363487 / ISBN 13: 9783764363482

Editore: Birkhauser Basel, 2000

Series: Progress in Mathematics. BIC Classification: PBM. Dimension: 235 x 155. Weight in Grams: 1100. . 2000. Hardback. . . . . Books ship from the US and Ireland. Codice articolo V9783764363482

Riassunto:

"…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

Contenuti: 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.

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Titolo: De Rham Cohomology of Differential Modules ...
Casa editrice: Birkhauser Basel
Data di pubblicazione: 2000
Legatura: Rilegato
Condizione: New