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Equidistribution of Weierstrass points on curves over non-Archimedean fields

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 نشر من قبل Omid Amini
 تاريخ النشر 2014
  مجال البحث
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 تأليف Omid Amini




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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.



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