Geodesic
Nice triples in the DVR context
Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 7, Tome 538 (2024), pp. 129-144

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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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     author = {I. A. Panin},
     title = {Nice triples in the {DVR} context},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {129--144},
     publisher = {mathdoc},
     volume = {538},
     year = {2024},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_538_a4/}
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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/