Status  Confirmed 
Seminar Series  MATHIHES 
Subjects  hepth 
Date  Wednesday 22 March 2017 
Time  10:30 
Institute  IHES 
Seminar Room  Amphithéâtre Léon Motchane 
Speaker's Last Name  SoulÉ 
Speaker's First Name  Christophe 
Speaker's Email Address  
Speaker's Institution  IHES 
Title  On the Arakelov theory of arithmetic surfaces (4/4) 
Abstract  Let X be a semistable arithmetic surface of genus at least two and ω the relative dualizing sheaf of X, equipped with the Arakelov metric. Parshin and MoretBailly have conjectured an upper bound for the arithmetic selfintersection of ω. They proved that a weak form of the abc conjecture follows from this inequality. We shall discuss a way of making their conjecture more precise in order that it implies the full abc conjecture (a proof of which has been announced by Mochizuki). 
arXiv Preprint Number  
Comments  Cours de l'IHES 
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