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On the normalized arithmetic Hilbert function

Posted in
Speaker: 
Mounir Hajli
Affiliation: 
University Moulay Ismail, Maroc/MPIM
Date: 
Wed, 2017-03-22 14:15 - 15:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

 Let X be a projective variety of dimension n defined over a number field.  Philippon and Sombra introduced   the normalized arithmetic Hilbert function of X. This function measures the binary complexity of X. When X is toric, a result of Philippon and Sombra shows that the asymptotic of this function is related to the normalized height of X. After a brief overview of
the theory of heights, I will show that the normalized arithmetic Hilbert function admits an asymptotic expansion the leading coefficient is the normalized height of X . This gives a positive answer to a question raised by Philippon and Sombra.

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