Motivic Euler products in motivic statistics

article Motivic Euler products in motivic statistics published yes Margaret Bilu author 98C47862-10D5-11EA-BEDD-0F6F3DDC885E Sean Howe author TiBr department 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. Mathematical Sciences Publishers2021 eng Algebra and Number Theory Algebra & Number Theory 1937-0652 1944-7833 1910.0520710.2140/ant.2021.15.2195 1592195-2259 M. Bilu, S. Howe, Algebra & Number Theory 15 (2021) 2195–2259. 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. Mathematical Sciences Publishers. <a href="https://doi.org/10.2140/ant.2021.15.2195">https://doi.org/10.2140/ant.2021.15.2195</a> 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:<a href="https://doi.org/10.2140/ant.2021.15.2195">10.2140/ant.2021.15.2195</a>. Bilu M, Howe S. 2021. Motivic Euler products in motivic statistics. Algebra & Number Theory. 15(9), 2195–2259. Bilu M, Howe S. Motivic Euler products in motivic statistics. Algebra & Number Theory. 2021;15(9):2195-2259. doi:<a href="https://doi.org/10.2140/ant.2021.15.2195">10.2140/ant.2021.15.2195</a> Bilu, Margaret, and Sean Howe. “Motivic Euler Products in Motivic Statistics.” Algebra & Number Theory. Mathematical Sciences Publishers, 2021. <a href="https://doi.org/10.2140/ant.2021.15.2195">https://doi.org/10.2140/ant.2021.15.2195</a>. 152792024-04-03T08:12:59Z2026-08-06T11:10:09Z