On two theorems for flat, affine group schemes over a discrete valuation ring
Adrian Vasiu
Open Mathematics, Tome 3 (2005), p. 14-25 / Harvested from The Polish Digital Mathematics Library

We include short and elementary proofs of two theorems that characterize reductive group schemes over a discrete valuation ring, in a slightly more general context.

Publié le : 2005-01-01
EUDML-ID : urn:eudml:doc:268856
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     author = {Adrian Vasiu},
     title = {On two theorems for flat, affine group schemes over a discrete valuation ring},
     journal = {Open Mathematics},
     volume = {3},
     year = {2005},
     pages = {14-25},
     zbl = {1108.14034},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475652}
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Adrian Vasiu. On two theorems for flat, affine group schemes over a discrete valuation ring. Open Mathematics, Tome 3 (2005) pp. 14-25. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475652/

[1] S. Bosch, W. Lütkebohmert and M. Raynaud: Néron models, Springer-Verlag, 1990.

[2] A. Borel: “Linear algebraic groups”, Grad. Texts in Math., Vol. 126, Springer-Verlag, 1991.

[3] N. Bourbaki: Lie groups and Lie algebras, Springer-Verlag, 2002, Chapters 4–6.

[4] F. Bruhat and J. Tits: “Groupes réductifs, sur un corps local: I Données radicielles valuées”, Inst. Hautes Études Sci. Publ. Math., Vol. 41, (1972), pp. 5–251.

[5] M. Demazure, A. Grothendieck and ét al.: Schémas en groupes. Vol. I–III, Lecture Notes in Math., Vol. 151–153, Springer-Verlag, 1970.

[6] A. Grothendieck: “Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schéma (Quatrième Partie)”, Inst. Hautes Études Sci. Publ. Math., Vol. 32, (1967).

[7] G. Hiss: “Die adjungierten Darstellungen der Chevalley-Gruppen”,Arch. Math.,Vol. 42, (1982),pp. 408–416. http://dx.doi.org/10.1007/BF01190689 | Zbl 0532.20022

[8] J.E. Humphreys: Conjugacy classes in semisimple algebraic groups, In: Math. Surv. and Monog., Vol. 43: Amer. Math. Soc., Providence, 1995. | Zbl 0834.20048

[9] J.C. Jantzen: Representations of algebraic groups. Second edition., In: Math. Surveys and Monog., Vol. 107, Amer. Math. Soc., Providence, 2000.

[10] H. Matsumura: Commutative algebra. Second edition. The Benjamin/Cummings Publ. Co., Inc., Reading, Massachusetts, 1980. | Zbl 0441.13001

[11] R. Pink: “Compact subgroups of linear algebraic groups”,J. of Algebra,Vol. 206, (1998),pp. 438–504. http://dx.doi.org/10.1006/jabr.1998.7439

[12] G. Prasad and J.-K. Yu: On quasi-reductive group schemes, math.NT/0405381, 34 pages revision, June 2004.

[13] A. Vasiu: “Integral canonical models of Shimura varieties of preabelian type”, Asian J. Math., Vol. 3(2), (1999), pp. 401–518.

[14] A. Vasiu: “Surjectivity criteria for p-adic representations, Part I”,Manuscripta Math.,Vol. 112(3), (2003),pp. 325–355. http://dx.doi.org/10.1007/s00229-003-0402-4 | Zbl 1117.11064