Conference in Number Theory on the occasion of the 70th birthday of Sergei Vladirimovich Vostokov

Talk, May 22nd : Some local-global arithmetic geometry

The  main topic is : local global principles for homogeneous spaces
of connected linear algebraic groups over the function field of a curve
over a the field of fractions of a complete discrete valuation ring

Some   documents related to my talk, with some links

Notes from talks :

JLCT, Quadrics over function fields in one (or more) variables over a p-adic field,
a survey talk in Bonn and Grenoble
 
JLCT, Higher reciprocity laws and rational points, a talk in Amsterdam

R. Parimala,  talk at the  ICM 2010 in Hyderabad

Papers :

D. Harbater, D. Krashen and J. Hartmann, Applications of patching to quadratic forms
and central simple algebras

and several papers by the three authors  to be found in particular on D. Harbater's homepage

JLCT, R. Parimala and V. Suresh, Patching and local-global principles for homogeneous spaces over function fields of p-adic curves

JLCT, R. Parimala and V. Suresh, Lois de réciprocité supérieures et points rationnels

D. Harari and T. Szamuely, Local-global questions for tori over p-adic function fields

D. Harari, C. Scheiderer and T. Szamuely, Weak approximation for tori over p-adic function fields

JLCT et D. Harari, Dualité et principe local-global pour les tores sur une courbe sur C((t))

to be found on the homepages of Harari and of Szamuely

D. Izquierdo, Théorèmes de dualité pour les corps de fonctions sur les corps locaux supérieurs

and various papers on his homepage

Yong Hu, various papers on his homepage