Motivic Euler products in motivic statistics

Bilu M, Howe S. 2021. Motivic Euler products in motivic statistics. Algebra & Number Theory. 15(9), 2195–2259.

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Journal Article | Published | English
Author
Bilu, MargaretISTA; Howe, Sean
Department
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.
Publishing Year
Date Published
2021-12-23
Journal Title
Algebra & Number Theory
Volume
15
Issue
9
Page
2195-2259
ISSN
eISSN
IST-REx-ID

Cite this

Bilu M, Howe S. Motivic Euler products in motivic statistics. Algebra & Number Theory. 2021;15(9):2195-2259. doi:10.2140/ant.2021.15.2195
Bilu, M., & Howe, S. (2021). Motivic Euler products in motivic statistics. Algebra & Number Theory. Mathematical Sciences Publishers. https://doi.org/10.2140/ant.2021.15.2195
Bilu, Margaret, and Sean Howe. “Motivic Euler Products in Motivic Statistics.” Algebra & Number Theory. Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/ant.2021.15.2195.
M. Bilu and S. Howe, “Motivic Euler products in motivic statistics,” Algebra & Number Theory, vol. 15, no. 9. Mathematical Sciences Publishers, pp. 2195–2259, 2021.
Bilu M, Howe S. 2021. Motivic Euler products in motivic statistics. Algebra & Number Theory. 15(9), 2195–2259.
Bilu, Margaret, and Sean Howe. “Motivic Euler Products in Motivic Statistics.” Algebra & Number Theory, vol. 15, no. 9, Mathematical Sciences Publishers, 2021, pp. 2195–259, doi:10.2140/ant.2021.15.2195.
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