Bücher Wenner
Wer wird Cosplay Millionär?
29.11.2024 um 19:30 Uhr
De Rham Cohomology of Differential Modules on Algebraic Varieties
von Yves André, Maurizio Cailotto, Francesco Baldassarri
Verlag: Springer International Publishing
Reihe: Progress in Mathematics Nr. 189
Hardcover
ISBN: 978-3-030-39721-0
Auflage: 2nd ed. 2020
Erschienen am 17.07.2021
Sprache: Englisch
Format: 235 mm [H] x 155 mm [B] x 15 mm [T]
Gewicht: 394 Gramm
Umfang: 256 Seiten

Preis: 128,39 €
keine Versandkosten (Inland)


Dieser Titel wird erst bei Bestellung gedruckt. Eintreffen bei uns daher ca. am 16. November.

Der Versand innerhalb der Stadt erfolgt in Regel am gleichen Tag.
Der Versand nach außerhalb dauert mit Post/DHL meistens 1-2 Tage.

klimaneutral
Der Verlag produziert nach eigener Angabe noch nicht klimaneutral bzw. kompensiert die CO2-Emissionen aus der Produktion nicht. Daher übernehmen wir diese Kompensation durch finanzielle Förderung entsprechender Projekte. Mehr Details finden Sie in unserer Klimabilanz.
Inhaltsverzeichnis
Klappentext

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.



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 cohomology¿ refers to the hypercohomology of the De Rham complex of a connection with respect to a smooth morphism of algebraic varieties, equipped with the Gauss-Manin connection. This simplified approach suffices to establish the stability of crucial properties of connections based on higher direct images. The main technical tools used include: Artin local decomposition of a smooth morphism in towers of elementary fibrations, and spectral sequences associated with affine coverings and with composite functors.


andere Formate
weitere Titel der Reihe