On two theorems for flat, affine group schemes over a discrete valuation ring

Adrian Vasiu

Open Mathematics (2005)

  • Volume: 3, Issue: 1, page 14-25
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Adrian Vasiu. "On two theorems for flat, affine group schemes over a discrete valuation ring." Open Mathematics 3.1 (2005): 14-25. <http://eudml.org/doc/268856>.

@article{AdrianVasiu2005,
abstract = {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.},
author = {Adrian Vasiu},
journal = {Open Mathematics},
keywords = {11G10; 11G18; 14F30; 14G35; 14G40; 14K10; 14J10},
language = {eng},
number = {1},
pages = {14-25},
title = {On two theorems for flat, affine group schemes over a discrete valuation ring},
url = {http://eudml.org/doc/268856},
volume = {3},
year = {2005},
}

TY - JOUR
AU - Adrian Vasiu
TI - On two theorems for flat, affine group schemes over a discrete valuation ring
JO - Open Mathematics
PY - 2005
VL - 3
IS - 1
SP - 14
EP - 25
AB - 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.
LA - eng
KW - 11G10; 11G18; 14F30; 14G35; 14G40; 14K10; 14J10
UR - http://eudml.org/doc/268856
ER -

References

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  5. [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. [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). 
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  9. [9] J.C. Jantzen: Representations of algebraic groups. Second edition., In: Math. Surveys and Monog., Vol. 107, Amer. Math. Soc., Providence, 2000. 
  10. [10] H. Matsumura: Commutative algebra. Second edition. The Benjamin/Cummings Publ. Co., Inc., Reading, Massachusetts, 1980. Zbl0441.13001
  11. [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. [12] G. Prasad and J.-K. Yu: On quasi-reductive group schemes, math.NT/0405381, 34 pages revision, June 2004. 
  13. [13] A. Vasiu: “Integral canonical models of Shimura varieties of preabelian type”, Asian J. Math., Vol. 3(2), (1999), pp. 401–518. 
  14. [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 Zbl1117.11064

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