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UID:news2086@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20261013T104452
DTSTART;TZID=Europe/Zurich:20261203T141500
SUMMARY:Number Theory Seminar: Antonio Fozzati (University College Dublin)
DESCRIPTION:Uniformity in the Bogomolov conjecture\\r\\nAbstract: The Bogom
 olov Conjecture\, proved by Ullmo and Zhang\, classifies the torsion subva
 rieties of an abelian variety as the subvarieties of small Arakelov height
 .This raises the question whether an explicit positive lower bound can be 
 given for the heights of non-torsion subvarieties. This question has been 
 addressed by David and Philippon. More recently\, Kuehne and Yuan showed i
 ndependently the existence of non-explicit\, but uniform bounds using tech
 niques from Arakelov theory. Even more\, Yuan proved lower bounds that are
  actually better than uniform. Before this\, similar bounds have been only
  obtained in the case of self-products of an elliptic curve through relate
 d work of David and Philippon.\\r\\nAfter giving an overview of the result
 s mentioned\, I will present the ideas used in the proof of the latter res
 ult. I will conclude by sketching how to improve upon this proof by replac
 ing the construction of an auxiliary function with a motivated use of tech
 niques of Arakelov Theory. This allows to improve the uniform bounds given
  by David and Philippon.\\r\\nSeminarraum 05.002\, Spiegelgasse 5
X-ALT-DESC:<h2>Uniformity in the Bogomolov conjecture</h2>\n<p>Abstract: Th
 e Bogomolov Conjecture\, proved by Ullmo and Zhang\, classifies the torsio
 n subvarieties of an abelian variety as the subvarieties of small Arakelov
  height.<br />This raises the question whether an explicit positive lower 
 bound can be given for the heights of non-torsion subvarieties. This quest
 ion has been addressed by David and Philippon. More recently\, Kuehne and 
 Yuan showed independently the existence of non-explicit\, but uniform boun
 ds using techniques from Arakelov theory. Even more\, Yuan proved lower bo
 unds that are actually better than uniform. Before this\, similar bounds h
 ave been only obtained in the case of self-products of an elliptic curve t
 hrough related work of David and Philippon.</p>\n<p>After giving an overvi
 ew of the results mentioned\, I will present the ideas used in the proof o
 f the latter result. I will conclude by sketching how to improve upon this
  proof by replacing the construction of an auxiliary function with a motiv
 ated use of techniques of Arakelov Theory. This allows to improve the unif
 orm bounds given by David and Philippon.</p>\n<p>Seminarraum 05.002\, Spie
 gelgasse 5</p>\n\n
DTEND;TZID=Europe/Zurich:20261203T151500
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