Vol. 15, No. 9, 2021

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
Motivic Euler products in motivic statistics

Margaret Bilu and Sean Howe

Vol. 15 (2021), No. 9, 2195–2259

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.

Bertini problems, Grothendieck ring of varieties, motivic probability, radicial surjective morphisms
Mathematical Subject Classification 2010
Primary: 14G10
Secondary: 55R80
Received: 3 December 2019
Revised: 1 February 2021
Accepted: 17 March 2021
Published: 23 December 2021
Margaret Bilu
Institute of Science and Technology Austria
Am Campus 1
Sean Howe
Department of Mathematics
University of Utah
Salt Lake City, UT
United States