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

Volume 18, 1 issue

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
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
The Manin–Mumford conjecture and the Tate–Voloch conjecture for a product of Siegel moduli spaces

Congling Qiu

Vol. 17 (2023), No. 5, 981–1016

We use perfectoid spaces associated to abelian varieties and Siegel moduli spaces to study torsion points and ordinary CM points. We reprove the Manin–Mumford conjecture, i.e., Raynaud’s theorem. We also prove the Tate–Voloch conjecture for a product of Siegel moduli spaces, namely ordinary CM points outside a closed subvariety can not be p-adically too close to it.

Manin–Mumford conjecture, Tate–Voloch conjecture, CM points, Siegel moduli spaces, perfectoid spaces
Mathematical Subject Classification
Primary: 11G10, 11G18, 14G35, 14G45, 14K12
Received: 12 February 2021
Revised: 27 March 2022
Accepted: 6 July 2022
Published: 9 May 2023
Congling Qiu
Department of Mathematics
Yale University
New Haven, CT
United States

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