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Motivic Euler products
in motivic statistics
Margaret Bilu and Sean Howe |
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Vol. 15 (2021), No. 9, 2195–2259
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Abstract |
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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. |
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Keywords
Bertini problems, Grothendieck ring of varieties, motivic
probability, radicial surjective morphisms
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Mathematical Subject Classification 2010
Primary: 14G10
Secondary: 55R80
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Milestones
Received: 3 December 2019
Revised: 1 February 2021
Accepted: 17 March 2021
Published: 23 December 2021
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Authors |
| Margaret Bilu | |
| Institute of Science and Technology
Austria Am Campus 1 Klosterneuburg Austria |
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| Sean Howe | |
| Department of Mathematics University of Utah Salt Lake City, UT United States |
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