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On Galois cohomology of semisimple groups over local and global fields of positive characteristic, III

Abstract

We extend some well-known results on Galois cohomology in its relation with weak approximation for connected linear algebraic groups over number fields to the case of global fields of positive characteristic. Some applications are considered.

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Notes

  1. In fact, such extensions have been considered first in Ono’s paper in Annals of Math. v. 82(1965), 88–111, p. 97, and in the literature it appears in relation with “crossed diagrams”.

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Acknowledgments

I would like to express my sincerest thanks to the referee for his/her careful reading and many constructive suggestions which help to improve the readability of the paper. This research is funded in part by VIASM and Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2011.40.

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Correspondence to Nguyêñ Quôć Thǎńg.

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Thǎńg, N.Q. On Galois cohomology of semisimple groups over local and global fields of positive characteristic, III. Math. Z. 275, 1287–1315 (2013). https://doi.org/10.1007/s00209-013-1183-4

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Mathematics Subject Classification (2000)

  • Primary 11E72
  • Secondary 18G50
  • 20G10