Author | Andrรฉ, Yves. author |
---|---|
Title | De Rham Cohomology of Differential Modules on Algebraic Varieties [electronic resource] / by Yves Andrรฉ, Francesco Baldassarri |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2001 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8336-8 |
Descript | VII, 214 p. online resource |
1 Regularity in several variables -- ยง1 Geometric models of divisorially valued function fields -- ยง2 Logarithmic differential operators -- ยง3 Connections regular along a divisor -- ยง4 Extensions with logarithmic poles -- ยง5 Regular connections: the global case -- ยง6 Exponents -- Appendix A: A letter of Ph. Robba (Nov. 2, 1984) -- Appendix B: Models and log schemes -- 2 Irregularity in several variables -- ยง1 Spectral norms -- ยง2 The generalized Poincarรฉ-Katz rank of irregularity -- ยง3 Some consequences of the Turrittin-Levelt-Hukuhara theorem -- ยง4 Newton polygons -- ยง5 Stratification of the singular locus by Newton polygons -- ยง6 Formal decomposition of an integrable connection at a singular divisor -- ยง7 Cyclic vectors, indicial polynomials and tubular neighborhoods -- 3 Direct images (the Gauss-Manin connection) -- ยง1 Elementary fibrations -- ยง2 Review of connections and De Rham cohomology -- ยง3 Dรฉvissage -- ยง4 Generic finiteness of direct images -- ยง5 Generic base change for direct images -- ยง6 Coherence of the cokernel of a regular connection -- ยง7 Regularity and exponents of the cokernel of a regular connection -- ยง8 Proof of the main theorems: finiteness, regularity, monodromy, base change (in the regular case) -- Appendix C: Berthelotโs comparison theorem on OXDX-linear duals -- Appendix D: Introduction to Dworkโs algebraic dual theory -- 4 Complex and p-adic comparison theorems -- ยง1 Review of analytic connections and De Rham cohomology -- ยง2 Abstract comparison criteria -- ยง3 Comparison theorem for algebraic vs.complex-analytic cohomology -- ยง4 Comparison theorem for algebraic vs. rigid-analytic cohomology (regular coefficients) -- ยง5 Rigid-analytic comparison theorem in relative dimension one -- ยง6 Comparison theorem for algebraic vs. rigid-analytic cohomology (irregular coefficients) -- ยง7 The relative non-archimedean Turrittin theorem -- Appendix E: Riemannโs โexistence theoremโ in higher dimension, an elementary approach -- References