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Shafarevich-Tate groups

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Shafarevich-Tate groups/ by M.L. Brown.
Author:	Brown, M. L.
Published:	Cham :Springer Nature Switzerland : : 2025.,
Description:	x, 314 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer Nature eBook
Subject:	Shafarevich maps. -
Online resource:	https://doi.org/10.1007/978-3-031-71893-9
ISBN:	9783031718939

Shafarevich-Tate groups
Brown, M. L.

Shafarevich-Tate groups[electronic resource] /by M.L. Brown. - Cham :Springer Nature Switzerland :2025. - x, 314 p. :ill. (some col.), digital ;24 cm. - Frontiers in mathematics,1660-8054. - Frontiers in mathematics..

Preliminaries -- Elliptic curves; Drinfeld modules; Shimura curves, Elliptic spaces -- Complex multiplication, Heegner points, CM points -- Local fields and local conditions -- Global fields and Selmer structures -- Euler systems -- Kolyvagin systems -- Selmer groups and Kolyvagin systems.

This monograph explores the finiteness and structure of Shafarevich-Tate groups of abelian varieties over global fields of any characteristic. Readers will better understand how the methods of Euler systems and Kolyvagin systems can be adapted to Heegner points and CM points. Also offered is a comprehensive overview of the most important classical and recent results on these objects. Shafarevich-Tate Groups will be a valuable resource to those interested in this active area of research.

ISBN: 9783031718939

Standard No.: 10.1007/978-3-031-71893-9doiSubjects--Topical Terms:

1488490
Shafarevich maps.

LC Class. No.: QA360

Dewey Class. No.: 511.326

Shafarevich-Tate groups
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490 1 $a Frontiers in mathematics, $x 1660-8054
505 0 $a Preliminaries -- Elliptic curves; Drinfeld modules; Shimura curves, Elliptic spaces -- Complex multiplication, Heegner points, CM points -- Local fields and local conditions -- Global fields and Selmer structures -- Euler systems -- Kolyvagin systems -- Selmer groups and Kolyvagin systems.
520 $a This monograph explores the finiteness and structure of Shafarevich-Tate groups of abelian varieties over global fields of any characteristic. Readers will better understand how the methods of Euler systems and Kolyvagin systems can be adapted to Heegner points and CM points. Also offered is a comprehensive overview of the most important classical and recent results on these objects. Shafarevich-Tate Groups will be a valuable resource to those interested in this active area of research.
650 0 $a Shafarevich maps. $3 1488490
650 0 $a Abelian groups. $3 768922
650 1 4 $a Number Theory. $3 672023
650 2 4 $a Algebraic Geometry. $3 670184
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830 0 $a Frontiers in mathematics. $3 888364
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