國立虎尾科技大學 |

De Rham Cohomology of Differential Modules on Algebraic Varieties

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	De Rham Cohomology of Differential Modules on Algebraic Varieties/ by Yves André, Francesco Baldassarri, Maurizio Cailotto.
作者:	André, Yves.
其他作者:	Baldassarri, Francesco.
面頁冊數:	XIV, 241 p.online resource. :
Contained By:	Springer Nature eBook
標題:	Algebraic geometry. -
電子資源:	https://doi.org/10.1007/978-3-030-39719-7
ISBN:	9783030397197

De Rham Cohomology of Differential Modules on Algebraic Varieties
André, Yves.

De Rham Cohomology of Differential Modules on Algebraic Varieties[electronic resource] /by Yves André, Francesco Baldassarri, Maurizio Cailotto. - 2nd ed. 2020. - XIV, 241 p.online resource. - Progress in Mathematics,1890743-1643 ;. - Progress in Mathematics,312.

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.

ISBN: 9783030397197

Standard No.: 10.1007/978-3-030-39719-7doiSubjects--Topical Terms:

1255324
Algebraic geometry.

LC Class. No.: QA564-609

Dewey Class. No.: 516.35

De Rham Cohomology of Differential Modules on Algebraic Varieties
LDR:05006nam a22004095i 4500 001 1025351
003 DE-He213
005 20200716110521.0
007 cr nn 008mamaa
008 210318s2020 gw | s |||| 0|eng d
020 $a 9783030397197 $9 978-3-030-39719-7
024 7 $a 10.1007/978-3-030-39719-7 $2 doi
035 $a 978-3-030-39719-7
050 4 $a QA564-609
072 7 $a PBMW $2 bicssc
072 7 $a MAT012010 $2 bisacsh
072 7 $a PBMW $2 thema
082 0 4 $a 516.35 $2 23
100 1 $a André, Yves. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1321613
245 1 0 $a De Rham Cohomology of Differential Modules on Algebraic Varieties $h [electronic resource] / $c by Yves André, Francesco Baldassarri, Maurizio Cailotto.
250 $a 2nd ed. 2020.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2020.
300 $a XIV, 241 p. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Progress in Mathematics, $x 0743-1643 ; $v 189
505 0 $a 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.
520 $a 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.
650 0 $a Algebraic geometry. $3 1255324
650 0 $a Functions of complex variables. $3 528649
650 0 $a Commutative algebra. $3 672047
650 0 $a Commutative rings. $3 672474
650 1 4 $a Algebraic Geometry. $3 670184
650 2 4 $a Several Complex Variables and Analytic Spaces. $3 672032
650 2 4 $a Commutative Rings and Algebras. $3 672054
700 1 $a Baldassarri, Francesco. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1321614
700 1 $a Cailotto, Maurizio. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1321615
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030397180
776 0 8 $i Printed edition: $z 9783030397203
776 0 8 $i Printed edition: $z 9783030397210
830 0 $a Progress in Mathematics, $x 0743-1643 ; $v 312 $3 1258196
856 4 0 $u https://doi.org/10.1007/978-3-030-39719-7
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)