De Rham cohomology of differential modules on algebraic varieties

Author(s)

Bibliographic Information

De Rham cohomology of differential modules on algebraic varieties

Yves André, Francesco Baldassarri, Maurizio Cailotto

(Progress in mathematics, v. 189)

Birkhäuser, c2020

2nd ed

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Note

"This book is published unde the imprint Birkhäuser, www.birkhause-science.com by the registered company Springer Nature Switzerland AG"--T.p. verso

Includes bibliographical references (p. 231-237) 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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Details

  • NCID
    BC0139085X
  • ISBN
    • 9783030397180
  • LCCN
    00044433
  • Country Code
    sz
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cham
  • Pages/Volumes
    xiv, 241 p.
  • Size
    25 cm
  • Parent Bibliography ID
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