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000938697 019__ $$a1178998383$$a1182462452$$a1182923148$$a1183937741
000938697 020__ $$a9783030397197$$q(electronic book)
000938697 020__ $$a303039719X$$q(electronic book)
000938697 020__ $$z9783030397180
000938697 0247_ $$a10.1007/978-3-030-39719-7$$2doi
000938697 0248_ $$a10.1007/978-3-030-39
000938697 035__ $$aSP(OCoLC)on1181835860
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000938697 08204 $$a514/.23$$223
000938697 1001_ $$aAndré, Yves,$$d1959-
000938697 24510 $$aDe Rham cohomology of differential modules on algebraic varieties /$$cYves André, Francesco Baldassarri, Maurizio Cailotto.
000938697 250__ $$a2nd ed.
000938697 260__ $$aCham :$$bBirkhäuser,$$c2020.
000938697 300__ $$a1 online resource (250 pages).
000938697 336__ $$atext$$btxt$$2rdacontent
000938697 337__ $$acomputer$$bc$$2rdamedia
000938697 338__ $$aonline resource$$bcr$$2rdacarrier
000938697 4901_ $$aProgress in Mathematics ;$$vv.189
000938697 506__ $$aAccess limited to authorized users.
000938697 520__ $$aThis is the revised second edition of the well-received book by the first two authors. It offers a systematic treatment of the theory of vector bundles with integrable connection on smooth algebraic varieties over a field of characteristic 0. Special attention is paid to singularities along divisors at infinity, and to the corresponding distinction between regular and irregular singularities. The topic is first discussed in detail in dimension 1, with a wealth of examples, and then in higher dimension using the method of restriction to transversal curves. The authors develop a new approach to classical algebraic/analytic comparison theorems in De Rham cohomology, and provide a unified discussion of the complex and the p-adic situations while avoiding the resolution of singularities. They conclude with a proof of a conjecture by Baldassarri to the effect that algebraic and p-adic analytic De Rham cohomologies coincide, under an arithmetic condition on exponents. As used in this text, the term "De Rham cohomology" refers to the hypercohomology of the De Rham complex of a connection with respect to a smooth morphism of algebraic varieties, equipped with the Gauss-Manin connection. This simplified approach suffices to establish the stability of crucial properties of connections based on higher direct images. The main technical tools used include: Artin local decomposition of a smooth morphism in towers of elementary fibrations, and spectral sequences associated with affine coverings and with composite functors.
000938697 588__ $$aDescription based on print version record.
000938697 650_0 $$aHomology theory.
000938697 650_0 $$aDifferential algebra.
000938697 650_0 $$aModules (Algebra)
000938697 7001_ $$aBaldassarri, F.$$q(Francesco),$$d1951-
000938697 7001_ $$aCailotto, Maurizio.
000938697 77608 $$iPrint version:$$aAndré, Yves$$tDe Rham Cohomology of Differential Modules on Algebraic Varieties$$dCham : Springer International Publishing AG,c2020$$z9783030397180
000938697 830_0 $$aProgress in mathematics (Boston, Mass.) ;$$vv. 189.
000938697 852__ $$bebk
000938697 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-030-39719-7$$zOnline Access$$91397441.1
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