Семинары: А. Н. Скоробогатов, Applications of additive combinatorics to conic and quadric bundles

СЕМИНАРЫ


Семинар отдела алгебры и отдела алгебраической геометрии (семинар И. Р. Шафаревича) 19 июня 2012 г. 15:00, г. Москва, МИАН, комн. 540 (ул. Губкина, 8)

Applications of additive combinatorics to conic and quadric bundles A. N. Skorobogatov
Аннотация: Methods of Green and Tao can be used to prove the Hasse principle and weak approximation for some special intersections of quadrics defined over $Q$ (arithmetic progressions in primes are replaced by arithmetic progressions in integers represented by binary quadratic forms). This implies that the Brauer-Manin obstruction controls weak approximation on conic bundles with an arbitrary number of degenerate fibres, all defined over $Q$, and some similar varieties. All previous results were restricted to conic bundle surfaces with a small number of degenerate fibres (up to 6). This is a joint work with Tim Browning and Lilian Matthiesen.