English

A short exact sequence

Algebraic Geometry 2021-01-19 v1 K-Theory and Homology

Abstract

Let R be a regular semi-local integral domain containing a field and K be its fraction field. Let mu: G --> T be an R-group schemes morphism between reductive R-group schemes, which is smooth as a scheme morphism. Suppose that T is an R-torus.Then the map T(R)/mu(G(R)) --> T(K)/mu(G(K)) is injective and certain purity theorem is true.These and other results are derived from an extended form of Grothendieck--Serre conjecture proven in the present paper for rings R as above.

Keywords

Cite

@article{arxiv.2101.07244,
  title  = {A short exact sequence},
  author = {Ivan Panin},
  journal= {arXiv preprint arXiv:2101.07244},
  year   = {2021}
}

Comments

arXiv admin note: text overlap with arXiv:1707.01763, arXiv:1406.1129

R2 v1 2026-06-23T22:17:16.213Z