De Rham cohomology of differential modules on algebraic varieties
Author(s)
Bibliographic Information
De Rham cohomology of differential modules on algebraic varieties
（Progress in mathematics, v. 189）
Birkhäuser Verlag, c2001
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Note
Includes bibliographical references (p. [209]-212) and index
Description and Table of Contents
Description
"...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
Table of Contents
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 Poincare-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 Devissage.- 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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