Equidistribution of Weierstrass points on curves over non-Archimedean   fields
  We prove equidistribution of Weierstrass points on Berkovich curves.   Let $X$ be a smooth proper curve of positive genus over a complete algebraically closed non-Archimedean field $K$ of equal characteristic zero with a non-trivial valuation.   Let $L$ be a line bundle of positive degree on $X$. The Weierstrass points of powers of $L$ are equidistributed according to the Zhang-Arakelov measure on the analytification $X^{an}$. This provides a non-Archimedean analogue of a theorem of Mumford and Neeman.   Along the way we provide a description of the reduction of Weierstrass points, answering a question of Eisenbud and Harris. 
Omid Amini
math.AG math.NT