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Transcendence and linear relations of 1-periods

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Transcendence and linear relations of 1-periods/ Annette Huber, Gisbert Wüstholz.
作者:	Huber, Annette.
其他作者:	Wüstholz, Gisbert.
出版者:	Cambridge ; New York, NY :Cambridge University Press, : 2022.,
面頁冊數:	xx, 243 p. :ill., digital ; : 23 cm.;
附註:	Title from publisher's bibliographic system (viewed on 07 Apr 2022).
標題:	Algebraic fields. -
電子資源:	https://doi.org/10.1017/9781009019729
ISBN:	9781009019729

Transcendence and linear relations of 1-periods
Huber, Annette.

Transcendence and linear relations of 1-periods[electronic resource] /Annette Huber, Gisbert Wüstholz. - Cambridge ; New York, NY :Cambridge University Press,2022. - xx, 243 p. :ill., digital ;23 cm. - Cambridge tracts in mathematics ;227. - Cambridge tracts in mathematics ;203..

Title from publisher's bibliographic system (viewed on 07 Apr 2022).

Basics on categories -- Homology and cohomology -- Commutative algebraic groups -- Lie groups -- The analytic subgroup theorem -- The formalism of the period conjecture -- Deligne's 1-motives -- Periods of 1-motives -- First examples -- On non-closed elliptic periods -- Periods of algebraic varieties -- Relations between periods -- Vanishing of periods of curves -- Dimension computations : an estimate -- Structure of the period space -- Incomplete periods of the third kind -- Elliptic curves -- Values of hypergeometric functions.

This exploration of the relation between periods and transcendental numbers brings Baker's theory of linear forms in logarithms into its most general framework, the theory of 1-motives. Written by leading experts in the field, it contains original results and finalises the theory of linear relations of 1-periods, answering long-standing questions in transcendence theory. It provides a complete exposition of the new theory for researchers, but also serves as an introduction to transcendence for graduate students and newcomers. It begins with foundational material, including a review of the theory of commutative algebraic groups and the analytic subgroup theorem as well as the basics of singular homology and de Rham cohomology. Part II addresses periods of 1-motives, linking back to classical examples like the transcendence of π, before the authors turn to periods of algebraic varieties in Part III. Finally, Part IV aims at a dimension formula for the space of periods of a 1-motive in terms of its data.

ISBN: 9781009019729Subjects--Topical Terms:

672441
Algebraic fields.

LC Class. No.: QA247.5 / .H83 2022

Dewey Class. No.: 512.73

Transcendence and linear relations of 1-periods
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505 0 $a Basics on categories -- Homology and cohomology -- Commutative algebraic groups -- Lie groups -- The analytic subgroup theorem -- The formalism of the period conjecture -- Deligne's 1-motives -- Periods of 1-motives -- First examples -- On non-closed elliptic periods -- Periods of algebraic varieties -- Relations between periods -- Vanishing of periods of curves -- Dimension computations : an estimate -- Structure of the period space -- Incomplete periods of the third kind -- Elliptic curves -- Values of hypergeometric functions.
520 $a This exploration of the relation between periods and transcendental numbers brings Baker's theory of linear forms in logarithms into its most general framework, the theory of 1-motives. Written by leading experts in the field, it contains original results and finalises the theory of linear relations of 1-periods, answering long-standing questions in transcendence theory. It provides a complete exposition of the new theory for researchers, but also serves as an introduction to transcendence for graduate students and newcomers. It begins with foundational material, including a review of the theory of commutative algebraic groups and the analytic subgroup theorem as well as the basics of singular homology and de Rham cohomology. Part II addresses periods of 1-motives, linking back to classical examples like the transcendence of π, before the authors turn to periods of algebraic varieties in Part III. Finally, Part IV aims at a dimension formula for the space of periods of a 1-motive in terms of its data.
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