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Seminar of the Department of Algebra and of the Department of Algebraic Geometry (Shafarevich Seminar)
June 19, 2012 15:00, Moscow, Steklov Mathematical Institute, room 540 (Gubkina 8)
 


Applications of additive combinatorics to conic and quadric bundles

A. N. Skorobogatov

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Abstract: 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.

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