93 citations · 237 across the 17 of their papers we have counts for
19 papers
Local-global principles for constant reductive groups over semi-global fields
Jean-Louis Colliot-Thélène, David Harbater, Julia Hartmann +3
We study local-global principles for torsors under reductive linear algebraic groups over semi-global fields; i.e., over one variable function fields over complete discretely value…
Local-global principles for tori over arithmetic curves
Jean-Louis Colliot-Thélène, David Harbater, Julia Hartmann +3
In this paper we study local-global principles for tori over semi-global fields, which are one variable function fields over complete discretely valued fields. In particular, we sh…
Brauer-Manin obstruction for Markoff surfaces
J. -L. Colliot-Thélène, Dasheng Wei, Fei Xu
Ghosh and Sarnak have studied integral points on surfaces defined by an equation x^2+y^2+z^2-xyz= m over the integers. For these affine surfaces, we systematically study the Brauer…
Non rationalité stable sur les corps quelconques
Jean-Louis Colliot-Thélène
This is a survey on (lack of) stable rationality over arbitrary fields (including algebraically closed fields). Topics addressed include: Rationality and unirationality, R-equivale…
Introduction to work of Hassett-Pirutka-Tschinkel and Schreieder
Jean-Louis Colliot-Thélène
In a smooth family of projective, complex varieties, stable rationality need not be preserved under generisation. This was proved by Hassett, Pirutka and Tschinkel upon use of the…
Local-Global Principles for Zero-Cycles on Homogeneous Spaces over Arithmetic Function Fields
Jean-Louis Colliot-Thélène, David Harbater, Julia Hartmann +3
We study the existence of zero-cycles of degree one on varieties that are defined over a function field of a curve over a complete discretely valued field. In particular, we show t…