Vol. 13, No. 2, 2019

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

Volume 14
Issue 2, 275–550
Issue 1, 1–274

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
Subscriptions
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
On rational singularities and counting points of schemes over finite rings

Itay Glazer

Vol. 13 (2019), No. 2, 485–500
Abstract

We study the connection between the singularities of a finite type -scheme X and the asymptotic point count of X over various finite rings. In particular, if the generic fiber X = X ×Spec Spec is a local complete intersection, we show that the boundedness of |X(pn)|pn dim X in p and n is in fact equivalent to the condition that X is reduced and has rational singularities. This paper completes a recent result of Aizenbud and Avni.

Keywords
rational singularities, complete intersection, analysis on p-adic varieties, asymptotic point count
Mathematical Subject Classification 2010
Primary: 14B05
Secondary: 14G05
Milestones
Received: 3 March 2018
Revised: 27 August 2018
Accepted: 24 December 2018
Published: 2 March 2019
Authors
Itay Glazer
Faculty of Mathematics and Computer Science
Weizmann Institute of Science
Rehovot 7610001
Israel