Download this article
 Download this article For screen
For printing
Recent Issues

Volume 18
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
Supersolvable descent for rational points

Yonatan Harpaz and Olivier Wittenberg

Vol. 18 (2024), No. 4, 787–814
DOI: 10.2140/ant.2024.18.787
Abstract

We construct an analogue of the classical descent theory of Colliot-Thélène and Sansuc in which algebraic tori are replaced with finite supersolvable groups. As an application, we show that rational points are dense in the Brauer–Manin set for smooth compactifications of certain quotients of homogeneous spaces by finite supersolvable groups. For suitably chosen homogeneous spaces, this implies the existence of supersolvable Galois extensions of number fields with prescribed norms, generalising work of Frei, Loughran and Newton.

Keywords
rational points, descent, inverse Galois problem
Mathematical Subject Classification
Primary: 11G35, 14G05, 14G12
Secondary: 12F12
Milestones
Received: 5 July 2022
Revised: 30 April 2023
Accepted: 14 June 2023
Published: 26 February 2024
Authors
Yonatan Harpaz
Institut Galilée
Université Sorbonne Paris Nord
Villetaneuse
France
Olivier Wittenberg
Institut Galilée
Université Sorbonne Paris Nord
Villetaneuse
France

Open Access made possible by participating institutions via Subscribe to Open.