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UID:5947@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20220929T143000
DTEND;TZID=Europe/Paris:20220929T153000
DTSTAMP:20241120T200703Z
URL:https://www.i2m.univ-amu.fr/evenements/lower-bounds-for-the-number-of-
 rational-points-on-curves-over-finite-fields/
SUMMARY:Christophe Ritzenthaler (IRMAR\, Université de Rennes 1 & CIMPA\, 
 Nice): Lower bounds for the number of rational points on curves over finit
 e fields
DESCRIPTION:Christophe Ritzenthaler: \nThe number of rational points on a c
 urve of genus g over Fq is upper bounded by 1+q+2g √q. But how good is t
 his bound in general? If the situation for fixed q and g going to infinit
 y has been studied for a while\, much less was known for g fixed and q goi
 ng to infinity. As a consequence of Katz-Sarnak theory\, we'll first get f
 or any given g &gt\; 0\, any ε &gt\; 0 and all q large enough\, the exist
 ence of a curve of genus g over Fq with at least 1 + q + (2g − ε)√q r
 ational points. Then using a distinct method\, we get weaker bounds of the
  form 1 + q + 4 √q − 32 but which are valid for any q &gt\; q0\, with 
 q0 explicit and g&gt\;1. \nThis is a joint work with Jonas Bergström\, Ev
 erett Howe and Elisa Lorenzo García.\n\n \n\n\nSite : \nhttps://sites.
 google.com/view/samuele-anni/home/s%C3%A9minaire-ati?authuser=0\n\n[su_spa
 cer size="10"]\nRendez-vous à côté de la machine à café au rez-de-cha
 ussée de l'ancienne BU.\n[su_spacer size="10"]\n\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Christophe_Ritzenthaler.jpg
CATEGORIES:Séminaire,Arithmétique et Théorie de l’Information
LOCATION:Luminy\, Campus des Sciences de Luminy\, Marseille\, 13009\, Franc
 e
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Campus des Sciences de Lumi
 ny\, Marseille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=Luminy:geo:0,0
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