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Transcendence and linear relations of 1-periods /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Transcendence and linear relations of 1-periods // Annette Huber, Gisbert Wüstholz..
Author:	Huber, Annette,
other author:	Wüstholz, Gisbert,
Description:	1 online resource (xx, 243 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 07 Apr 2022).
Subject:	Transcendental numbers. -
Online resource:	https://doi.org/10.1017/9781009019729
ISBN:	9781009019729 (ebook)

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

Transcendence and linear relations of 1-periods /Annette Huber, Gisbert Wüstholz.. - 1 online resource (xx, 243 pages) :digital, PDF file(s). - 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: 9781009019729 (ebook)Subjects--Topical Terms:

1405680
Transcendental numbers.

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

Dewey Class. No.: 512.7/3

Transcendence and linear relations of 1-periods /
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245 1 0 $a Transcendence and linear relations of 1-periods / $c Annette Huber, Gisbert Wüstholz..
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500 $a Title from publisher's bibliographic system (viewed on 07 Apr 2022).
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.
650 0 $a Transcendental numbers. $3 1405680
650 0 $a Motives (Mathematics) $3 857130
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830 0 $a Cambridge tracts in mathematics ; $v 203. $3 1238301
856 4 0 $u https://doi.org/10.1017/9781009019729