Algebraic Geometry Seminar
Thursday, April 9, 2009, 4:30pm, 119 Physics
Pete Clark (University of Georgia)
(Postponed to a later date) Algebraic Curves Violating the Hasse Principle

Abstract:

The celebrated "Hasse Principle" holds for plane conics over a number field, but generally not for algebraic curves of positive genus. Isolated examples of curves violating the Hasse Principle go back to Lind, Reichardt and Selmer in the 1940s and 1950s. Many more examples have been found since, and it now seems likely that the Hasse principle should, in some suitable sense, most often be false. However it is challenging to make, let alone prove, a precise statement to this effect. In talk I will discuss certain "anti-Hasse principles", some which are conjectural and others (more modest) which are known to hold. In particular I will address the problem of constructing curves of any given genus g >= 1 over any global field which violate the Hasse [video]

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