2 citations · 2 across the 2 of their papers we have counts for
5 papers
Pathologies of the Brauer-Manin obstruction
Jean-Louis Colliot-Thélène, Ambrus Pál, Alexei N. Skorobogatov
We construct a conic bundle over an elliptic curve over a real quadratic field that is a counterexample to the Hasse principle not explained by the étale Brauer-Manin obstruction.…
Good reduction of the Brauer-Manin obstruction
J. -L. Colliot-Thélène, A. N. Skorobogatov
For a smooth and projective variety over a number field with torsion free geometric Picard group and finite transcendental Brauer group we show that only the archimedean places, th…
Patching and local-global principles for homogeneous spaces over function fields of p-adic curves
J. -L. Colliot-Thélène, R. Parimala, V. Suresh
This is the final version, to appear in Commentarii Mathematici Helvetici.
Rational connectedness and Galois covers of the projective line
Jean-Louis Colliot-Thelene
Let k be a p-adic field. Some time ago, D. Harbater [9] proved that any finite group G may be realized as a regular Galois group over the rational function field in one variable k(…
Algebraic families of nonzero elements of Shafarevich-Tate groups
Jean-Louis Colliot-Thelene, Bjorn Poonen
We show that there exist non-trivial families of algebraic varieties for which all the fibers above rational points (or even above points of odd degree) are torsors of abelian vari…