De Rham Cohomology of Differential Modules on Algebraic Varieties. 2nd ed. 2020

種類:

電子ブック

責任表示:

by Yves André, Francesco Baldassarri, Maurizio Cailotto

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2020

著者名:

• André, Yves.
• Baldassarri, Francesco.
• Cailotto, Maurizio.
• SpringerLink (Online service)

シリーズ名:

Progress in Mathematics ; 189

ISBN:

9783030397197 [303039719X]    

注記:

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
This is the revised second edition of the well-received book by the first two authors. It offers a systematic treatment of the theory of vector bundles with integrable connection on smooth algebraic varieties over a field of characteristic 0. Special attention is paid to singularities along divisors at infinity, and to the corresponding distinction between regular and irregular singularities. The topic is first discussed in detail in dimension 1, with a wealth of examples, and then in higher dimension using the method of restriction to transversal curves. The authors develop a new approach to classical algebraic/analytic comparison theorems in De Rham cohomology, and provide a unified discussion of the complex and the p-adic situations while avoiding the resolution of singularities. They conclude with a proof of a conjecture by Baldassarri to the effect that algebraic and p-adic analytic De Rham cohomologies coincide, under an arithmetic condition on exponents. As used in this text, the term “De Rham cohomolo

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