Weak Approximation for Tori Over p-adic Function Fields

作者：Harari David; Scheiderer Claus; Szamuely Tamas^*

来源：International Mathematics Research Notices, 2015, 2015(10): 2751-2783.

DOI：10.1093/imrn/rnu019

We study local-global questions for Galois cohomology over the function field of a curve defined over a p-adic field, the main focus being weak approximation of rational points. We construct a 9-term Poitou-Tate-type exact sequence for tori over a field as above (and also a 12-term sequence for finite modules). Like in the number field case, part of the sequence can then be used to analyze the defect of weak approximation for a torus. We also show that the defect of weak approximation is controlled by a certain subgroup of the third unramified cohomology group of the torus.

• 出版日期2015