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.
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