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Seminar

MT Research Seminar: Local vs. finite Galois obstructions to rational points. March 04, 2014 (11:00 AM PST - 12:30 PM PST)
Parent Program: Model Theory, Arithmetic Geometry and Number Theory
Location: MSRI: Simons Auditorium
Speaker(s) Michael Larsen (Indiana University)
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Abstract/Media

Let X be a non-singular curve over a number field K.  Consider two kinds of obstructions to the existence of K-points on X: local obstructions (e.g., X has no points over R or over Q_p), and finite Galois obstructions (e.g., there exists an element s of Gal(\bar K/K) such that no element of X(\bar K) is s-stable).  I will ask whether these two obstructions are the same and discuss evidence coming from algebraic number theory, Diophantine geometry, and additive combinatorics.

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