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de Rham Cohomology of Differential Modules on Algebraic Varieties

de Rham Cohomology of Differential Modules on Algebraic Varieties


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About the Book

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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Product Details
  • ISBN-13: 9783030397180
  • Publisher: Springer International Publishing
  • Publisher Imprint: Birkhauser
  • Height: 234 mm
  • No of Pages: 241
  • Series Title: Progress in Mathematics
  • Weight: 589 gr
  • ISBN-10: 3030397181
  • Publisher Date: 17 Jul 2020
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Spine Width: 16 mm
  • Width: 156 mm


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