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Shafarevich-Tate groups

Brown, M. L.

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Shafarevich-Tate groups

Record Type:	Electronic resources : 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.
[NT 15003449]:	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.
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:

711338
Shafarevich maps.

LC Class. No.: QA360

Dewey Class. No.: 511.326

Shafarevich-Tate groups
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100 1 $a Brown, M. L. $3 3782714
245 1 0 $a Shafarevich-Tate groups $h [electronic resource] / $c by M.L. Brown.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Birkhäuser, $c 2025.
300 $a x, 314 p. : $b ill. (some col.), digital ; $c 24 cm.
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 711338
650 0 $a Abelian groups. $3 641259
650 1 4 $a Number Theory. $3 891078
650 2 4 $a Algebraic Geometry. $3 893861
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Frontiers in mathematics. $3 1535268
856 4 0 $u https://doi.org/10.1007/978-3-031-71893-9
950 $a Mathematics and Statistics (SpringerNature-11649)