Motivic Euler products in motivic statistics

Bilu, Margaret; Howe, Sean

doi:10.2140/ant.2021.15.2195

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

Motivic Euler products in motivic statistics

Margaret Bilu and Sean Howe

Vol. 15 (2021), No. 9, 2195–2259

DOI: 10.2140/ant.2021.15.2195

Abstract

We formulate and prove an analog of Poonen’s finite-field Bertini theorem with Taylor conditions that holds in the Grothendieck ring of varieties. This gives a broad generalization of the work of Vakil and Wood, who treated the case of smooth hypersurface sections, and is made possible by the use of motivic Euler products to write down candidate motivic probabilities. As applications, we give motivic analogs of many results in arithmetic statistics that have been proven using Poonen’s sieve, including work of Bucur and Kedlaya on complete intersections and Erman and Wood on semiample Bertini theorems.

Keywords

Bertini problems, Grothendieck ring of varieties, motivic probability, radicial surjective morphisms

Mathematical Subject Classification 2010

Primary: 14G10

Secondary: 55R80

Milestones

Received: 3 December 2019

Revised: 1 February 2021

Accepted: 17 March 2021

Published: 23 December 2021

Authors

Margaret Bilu
Institute of Science and Technology Austria Am Campus 1 Klosterneuburg Austria

Sean Howe
Department of Mathematics University of Utah Salt Lake City, UT United States

Vol. 15, No. 9, 2021