Supersolvable descent for rational points

Harpaz, Yonatan; Wittenberg, Olivier

doi:10.2140/ant.2024.18.787

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

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.

Vol. 18, No. 4, 2024