Geodesic
Nice triples in the DVR context
Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 7, Tome 538 (2024), pp. 129-144 Cet article a éte moissonné depuis la source Math-Net.Ru

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A theory of standard triples was invented by V. Voevodsky in [14] to construct the triangulated category of motives. Being inspired by that theory a theory of nice triples was invented in [7] in order to attack the Grothendieck–Serre conjecture and related problem. However both the mentioned theories were developed for smooth varieties over a field. In the present paper a theory of nice triples is developed for smooth schemes over a DVR. Theorem 1.4 is used in [12] as one of a major step in the proof of the Grothendieck–Serre conjecture in the constant mixed characteristic case. 
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I. A. Panin. Nice triples in the DVR context. Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 7, Tome 538 (2024), pp. 129-144. http://geodesic.mathdoc.fr/item/ZNSL_2024_538_a4/

[1] M. Artin, “Comparaison avec la cohomologie classique: cas d'un préschéma lisse”, Théorie des topos et cohomologie étale des schémas (SGA 4), v. 3, Lect. Notes Math., 305, Springer-Verlag, Berlin-New York, 1973 | Zbl

[2] J.-L. Colliot-Thélène, M. Ojanguren, “Espaces Principaux Homogènes Localement Triviaux”, Publ. Math. IHÉS, 75:2 (1992), 97–122 | DOI | MR | Zbl

[3] N. Guo, I. Panin, A Presentation theorem for smooth projective schemes over discrete valuation rings, 2023, arXiv: 2302.02818v1

[4] N. Guo, I. Panin, “Weak elementary fibrations”, St.Petersburg Math. Journal, 2023 (to appear) , arXiv: 2302.02837v1

[5] F. Morel, V. Voevodsky, “$A^1$-homotopy theory of schemes”, Publ. Math. IHÉS, 90 (1999), 45–143 | DOI | MR | Zbl

[6] M. Ojanguren, I. Panin, “Rationally trivial hermitian spaces are locally trivial”, Math. Z., 237 (2001), 181–198 | DOI | MR | Zbl

[7] I. Panin, A. Stavrova, N. Vavilov, “On Grothendieck—Serre's conjecture concerning principal $G$-bundles over reductive group schemes I”, Compositio Math., 151 (2015), 535–567 | DOI | MR | Zbl

[8] I. Panin, “Nice triples and moving lemmas for motivic spaces”, Izv. Math., 83:4 (2019), 796–829 | DOI | MR | Zbl

[9] I. Panin, “Proof of the Grothendieck–Serre conjecture on principal bundles over regular local rings containing a field”, Izvestiya Mathematics, 84:4 (2020), 780–795 | DOI | MR | Zbl

[10] I. Panin, “On Grothendieck–Serre conjecture concerning principal bundles”, Proceedings of the International Congress of Mathematicians (Rio de Janeiro 2018), v. 2, World Sci. Publ., Hackensack, NJ, 2018, 201–221 | MR | Zbl

[11] I. Panin, Moving lemmas in mixed characteristic and applications, arXiv: 2202.00896v1

[12] I. A. Panin, A. K. Stavrova, Constant case of the Grothendieck–Serre conjecture in mixed characteristic, Preprint, November 2024 | MR

[13] I. A. Panin, A. K. Stavrova, On the Gille theorem for the relative projective line, arXiv: 2305.16627v2

[14] V. Voevodsky, “Cohomological theory of presheaves with transfers”, Cycles, Transfers, and Motivic Homology Theories, Ann. Math. Studies, Princeton University Press, 2000 | MR