A non-Archimedean Weyl equidistribution theorem

Series: 
Algebra Seminar
Tuesday, January 19, 2010 - 16:00
1 hour (actually 50 minutes)
Location: 
Skiles 269
,  
Hunter College
Organizer: 
Weyl proved that if an N-dimensional real vector v has linearly independent coordinates over Q, then its integer multiples v, 2v, 3v, .... are uniformly distributed modulo 1.  Stated multiplicatively (via the exponential map), this can be viewed as a Haar-equidistribution result for the cyclic group generated by a point on the N-dimensional complex unit torus.  I will discuss an analogue of this result over a non-Archimedean field K, in which the equidistribution takes place on the N-dimensional Berkovich projective space over K.  The proof uses a general criterion for non-Archimedean equidistribution, along with a theorem of Mordell-Lang type for the group variety G_m^N over the residue field of K, which is due to Laurent.