We generalize Colliot-Thélène’s construction of flasque resolutions of reductive group schemes over a field to a broad class of base schemes.
@article{bwmeta1.element.doi-10_2478_s11533-013-0235-7,
author = {Cristian Gonz\'alez-Avil\'es},
title = {Flasque resolutions of reductive group schemes},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {1159-1176},
zbl = {1273.14090},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0235-7}
}
Cristian González-Avilés. Flasque resolutions of reductive group schemes. Open Mathematics, Tome 11 (2013) pp. 1159-1176. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0235-7/
[1] Artin M., Grothendieck A., Verdier J.L. (Eds.), Théorie des Topos et Cohomologie Étale des Schémas III, Séminaire de Géométrie Algébrique du Bois-Marie 1963-64 (SGA 4), Lecture Notes in Math., 305, Springer, Berlin-New York, 1973
[2] Borovoi M., Abelian Galois Cohomology of Reductive Groups, Mem. Amer. Math. Soc., 132(626), American Mathematical Society, Providence, 1998 | Zbl 0918.20037
[3] Borovoi M., The algebraic fundamental group of a reductive group scheme over an arbitrary base scheme, Appendix B, preprint available at http://arxiv.org/abs/1112.6020v1 [WoS]
[4] Bourbaki N., Commutative Algebra, Chapters 1–7, Elem. Math. (Berlin), Springer, Berlin, 1989
[5] Breen L., On the Classification of 2-Gerbes and 2-Stacks, Astérisque, 225, Soc. Math. France Inst. Henri Poincaré, Paris, 1994 | Zbl 0818.18005
[6] Colliot-Thélène J.-L., Résolutions flasques des groupes linéaires connexes, J. Reine Angew. Math., 2008, 618, 77–133
[7] Colliot-Thélène J.-L., Sansuc J.-J., La R-équivalence sur les tores, Ann. Sci. École Norm. Sup., 1977, 10(2), 175–229
[8] Colliot-Thélène J.-L., Sansuc J.-J., Principal homogeneous spaces under flasque tori: applications, J. Algebra, 1987, 106(1), 148–205 http://dx.doi.org/10.1016/0021-8693(87)90026-3[Crossref] | Zbl 0597.14014
[9] Conrad B., Reductive group schemes (SGA Summer school, 2011), available at http://math.stanford.edu/~conrad/papers/luminysga3.pdf
[10] Demazure M., Grothendieck A. (Eds.), Schémas en Groupes I–III, Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3), Lecture Notes in Math., 151-153, Springer, Berlin-Heidelberg-New York, 1970
[11] González-Avilés C.D. Quasi-abelian crossed modules and nonabelian cohomology, J. Algebra, 2012, 369, 235–255 http://dx.doi.org/10.1016/j.jalgebra.2012.07.031[WoS][Crossref]
[12] González-Avilés C., Abelian class groups of reductive group schemes, Israel J. Math. (in press), DOI: 10.1007/s11856-012-0147-4 [Crossref][WoS] | Zbl 1278.14064
[13] Grothendieck A., Éléments de Géométrie Algébrique IV. Étude Locale des Schémas et des Morphismes de Schémas, I, IV, Inst. Hautes Études Sci. Publ. Math., 20, 32, Paris, 1964, 1967 | Zbl 0136.15901
[14] Harder G., Halbeinfache Gruppenschemata über Dedekindringen, Invent. Math., 1967, 4(3), 165–191 http://dx.doi.org/10.1007/BF01425754[Crossref] | Zbl 0158.39502
[15] Milne J.S., Étale Cohomology, Princeton Math. Ser., 33, Princeton University Press, Princeton, 1980
[16] Milne J.S., Arithmetic Duality Theorems, 2nd ed., BookSurge, Charleston, 2006 | Zbl 1127.14001
[17] Raynaud M., Faisceaux amples sur les schémas en groupes et les espaces homogènes, Lecture Notes in Math., 119, Springer, Berlin-Heidelberg-New York, 1970 http://dx.doi.org/10.1007/BFb0059504[Crossref] | Zbl 0195.22701
[18] Sansuc J.-J., Groupe de Brauer et arithmétique des groupes algébriques linéaires sur un corps de nombres, J. Reine Angew. Math., 1981, 327, 12–80 | Zbl 0468.14007
[19] Weibel C.A., An Introduction to Homological Algebra, Cambridge Stud. Adv. Math., 38, Cambridge University Press, Cambridge, 1994 http://dx.doi.org/10.1017/CBO9781139644136[Crossref]