Voir la notice de l'article provenant de la source Math-Net.Ru
@article{AA_2019_31_1_a10, author = {A. E. Tsybyshev}, title = {A step toward the mixed-characteristic case of the {Grothendieck--Serre} conjecture}, journal = {Algebra i analiz}, pages = {246--254}, publisher = {mathdoc}, volume = {31}, number = {1}, year = {2019}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/AA_2019_31_1_a10/} }
A. E. Tsybyshev. A step toward the mixed-characteristic case of the Grothendieck--Serre conjecture. Algebra i analiz, Tome 31 (2019) no. 1, pp. 246-254. http://geodesic.mathdoc.fr/item/AA_2019_31_1_a10/
[1] Demazure M., Grothendieck A., et al., Séminaire de Géométrie Algébrique du Bois Marie 1962/64, Lecture Notes in Math., 152, Springer-Verlag, Berlin, 1970 | MR
[2] Grothendieck A., “Éléments de géométrie algébrique. III. Étude cohomologique des faisceaux cohérents. I–II”, Publ. Math. Inst. Hautes Études Sci., 11, 1961, 1–167 ; 17, 1963, 1–91 | MR | MR
[3] Grothendieck A., “Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. I–IV”, Publ. Math. Inst. Hautes Études Sci., 20, 1964, 1–259 ; 24, 1965, 1–231 ; 28, 1966, 1–255 ; 32, 1967, 1–361 | MR | MR | Zbl | MR | Zbl | MR | Zbl
[4] Mumford D., Fogarty J., Kirwan F., Geometric invariant theory, Ergeb. Math. Grenzgeb., 34, Third ed., Springer-Verlag, Berlin, 1994 | MR
[5] Thomason R. W., “Equivariant resolution, linearization, and Hilbert's fourteenth problem over arbitrary base schemes”, Adv. in Math., 65:1 (1987), 16–34 | DOI | MR | Zbl
[6] Colliot-Thélène J.-L., Ojanguren M., “Espaces principaux homogènes localement triviaux”, Publ. Math. Inst. Hautes Études Sci., 75, 1992, 97–122 | DOI | MR | Zbl
[7] Grothendieck A., “Technique de descente et théorèmes d'existence en géometrie algébrique. I. {G}énéralités. Descente par morphismes fidèlement plats”, Séminaire {B}ourbaki, 5, no. 190, Soc. Math. France, Paris, 1995, 299–327 | MR
[8] Nisnevich Y., “Espaces homogènes principaux rationnellement triviaux et arithmétique des schémas en groupes réductifs sur les anneaux de {D}edekind”, C. R. Acad. Sci. Paris Sér. I Math., 299:1 (1984), 5–8 | MR | Zbl
[9] Nisnevich Y., “Rationally trivial principal homogeneous spaces, purity and arithmetic of reductive group schemes over extensions of two-dimensional regular local rings”, C. R. Acad. Sci. Paris Sér. I Math., 309:10 (1989), 651–655 | MR | Zbl
[10] Raghunathan M. S., “Principal bundles admitting a rational section”, Invent. Math., 116:1–3 (1994), 409–423 | DOI | MR | Zbl
[11] Raghunathan M. S., “Erratum “Principal bundles admitting a rational section” [Invent. Math. 116 (1994), no. 1–3, 409–423]”, Invent. Math., 121:1 (1995), 223 | DOI | MR | Zbl
[12] Panin I., Stavrova A., Vavilov N., “On Grothendieck–Serre's conjecture concerning principal $G$-bundles over reductive group schemes. I”, Compos. Math., 151:3 (2015), 535–567 | DOI | MR | Zbl
[13] Panin I., Proof of Grothendieck–Serre conjecture on principal $G$-bundles over regular local rings containing a finite field, arXiv: 1406.0247
[14] Fedorov R., Panin I., “A proof of the Grothendieck–Serre conjecture on principial bundles over regular local rings containing infinite fields”, Publ. Math. Inst. Hautes Études Sci., 122, 2015, 169–193 | DOI | MR | Zbl