About: Gauss–Manin connection

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In mathematics, the Gauss–Manin connection is a connection on a certain vector bundle over a base space S of a family of algebraic varieties . The fibers of the vector bundle are the de Rham cohomology groups of the fibers of the family. It was introduced by Yuri Manin for curves S and by Alexander Grothendieck in higher dimensions.

Attributes	Values
rdfs:label	Gauss–Manin connection (en) Связность Гаусса — Манина (ru) Зв'язність Гаусса - Маніна (uk)
rdfs:comment	З розшаруванням, шари якого є гладкими многовидами (або гладкими алгебричними многовидами), можна пов'язати деяке розшарування з плоскою зв'язністю, що називається зв'язністю Гаусса — Маніна. (uk) С расслоением, слои которого являются гладкими многообразиями (или гладкими алгебраическими многообразиями), можно связать некоторое расслоение с плоской связностью, называемой свя́зностью Га́усса — Ма́нина. (ru) In mathematics, the Gauss–Manin connection is a connection on a certain vector bundle over a base space S of a family of algebraic varieties . The fibers of the vector bundle are the de Rham cohomology groups of the fibers of the family. It was introduced by Yuri Manin for curves S and by Alexander Grothendieck in higher dimensions. (en)
dcterms:subject	Algebraic geometry Connection (mathematics)
Wikipage page ID	4550529 (xsd:integer)
Wikipage revision ID	1087810613 (xsd:integer)
Link from a Wikipage to another Wikipage	Mirror symmetry conjecture De Rham cohomology D-module Connection (mathematics) Mathematics Elliptic curve Modularity theorem Yves André Publications Mathématiques de l'IHÉS Algebraic variety American Mathematical Society Differential equation Siegel G-function Algebraic geometry Connection (mathematics) Mixed Hodge module Grothendieck–Katz p-curvature conjecture Vector bundle Picard–Fuchs equation Transcendental number theory P-curvature Nicholas Katz Direct image of a sheaf Ehresmann fibration theorem Complex projective line dbr:Dwork_construction dbr:Meromorphic_connection
Link from a Wikipage to an external page	http://algant.eu/documents/theses/barrientos.pdf http://mi.mathnet.ru/eng/izv/v22/i6/p737 https://books.google.com/books%3Fid=fZ7ms3db_cMC https://projecteuclid.org/euclid.bams/1183531477 http://www.numdam.org/item%3Fid=PMIHES_1966__29__95_0
sameAs	Gauss–Manin connection Gauss–Manin connection Gauss–Manin connection Gauss–Manin connection Gauss–Manin connection
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Reflist dbt:Harvs dbt:Eom
authorlink	Alexander Grothendieck (en) Yuri Manin (en)
first	Alexander (en) Yuri (en)
last	Grothendieck (en) Manin (en)
year	1958 (xsd:integer) 1966 (xsd:integer)
has abstract	In mathematics, the Gauss–Manin connection is a connection on a certain vector bundle over a base space S of a family of algebraic varieties . The fibers of the vector bundle are the de Rham cohomology groups of the fibers of the family. It was introduced by Yuri Manin for curves S and by Alexander Grothendieck in higher dimensions. Flat sections of the bundle are described by differential equations; the best-known of these is the Picard–Fuchs equation, which arises when the family of varieties is taken to be the family of elliptic curves. In intuitive terms, when the family is locally trivial, cohomology classes can be moved from one fiber in the family to nearby fibers, providing the 'flat section' concept in purely topological terms. The existence of the connection is to be inferred from the flat sections. (en) З розшаруванням, шари якого є гладкими многовидами (або гладкими алгебричними многовидами), можна пов'язати деяке розшарування з плоскою зв'язністю, що називається зв'язністю Гаусса — Маніна. (uk) С расслоением, слои которого являются гладкими многообразиями (или гладкими алгебраическими многообразиями), можно связать некоторое расслоение с плоской связностью, называемой свя́зностью Га́усса — Ма́нина. (ru)
prov:wasDerivedFrom	wikipedia-en:Gauss–Manin_connection?oldid=1087810613&ns=0
page length (characters) of wiki page	8150 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Gauss–Manin_connection
is Link from a Wikipage to another Wikipage of	Algebraic analysis Jacobian ideal Yuri Manin Gauss-Manin connection Period (algebraic geometry) Local system Alexander Varchenko Kodaira–Spencer map List of Russian mathematicians List of Russian scientists List of things named after Carl Friedrich Gauss Isomonodromic deformation Hodge structure Hodge–Arakelov theory Grothendieck connection Grothendieck–Katz p-curvature conjecture Picard–Fuchs equation List of Russian people
is Wikipage redirect of	Gauss-Manin connection
is foaf:primaryTopic of	wikipedia-en:Gauss–Manin_connection

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