Smooth blowup square for motives with modulus. (English) Zbl 1484.14008
Summary: In this self-contained paper we prove that Voevodsky’s smooth blowup triangle of motives generalises to a smooth blowup triangle of motives with modulus.
MSC:
| 14C15 | (Equivariant) Chow groups and rings; motives |
| 14F42 | Motivic cohomology; motivic homotopy theory |
References:
| [1] | B. Kahn, H. Miyazaki, S. Saito and T. Yamazaki: Motives with modulus, I: Modulus sheaves with transfers for non-proper modulus pairs, Épijournal Géom. Algébrique 5 (2021), art. 1, 46 pp. · Zbl 1506.19002 |
| [2] | B. Kahn, H. Miyazaki, S. Saito and T. Yamazaki: Motives with modulus, II: Modulus sheaves with transfers for proper modulus pairs, Épijournal Géom. Algébrique 5 (2021), art. 2, 31 pp. · Zbl 1468.19005 |
| [3] | B. Kahn, H. Miyazaki, S. Saito, and T. Yamazaki, Motives with modulus, III: The categories of motives, Ann. K-Theory (to appear); arXiv:2011.11859. |
| [4] | K. Matsumoto, Gysin triangles in the category of motifs with modulus, J. Inst. Math. Jussieu (online, 2022). |
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| [7] | V. Voevodsky, Homotopy theory of simplicial sheaves in completely decom-posable topologies, J. Pure Appl. Algebra 214 (2010), 1384-1398. · Zbl 1194.55020 |
| [8] | V. Voevodsky, Triangulated categories of motives over a field, in: Cycles, Transfers, and Motivic Homology Theories, Ann. of Math. Stud. 143, Prince-ton Univ. Press, Princeton, NJ, 2000, 188-238. · Zbl 1019.14009 |
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