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UID:8525@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20250121T140000
DTEND;TZID=Europe/Paris:20250121T150000
DTSTAMP:20250116T220313Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-194/
SUMMARY:Marco Sangiovanni Vincentelli (Princeton): Selmer groups\, p-adic L
 -functions and Euler Systems: A Unified Framework
DESCRIPTION:Marco Sangiovanni Vincentelli: \n\n\n\n\n\n\nSelmer groups are 
 key invariants attached to p-adic Galois representations. The Bloch—Kato
  conjecture predicts a precise relationship between the size of certain Se
 lmer groups and the leading term of the L-functionof the Galois representa
 tion under consideration. In particular\, when the L-function does not hav
 e a zero at s=0\, it predicts that the Selmer group is finite and its orde
 r is controlled by the value of the L-function at s=0. Historically\, one 
 of the most powerful tools to prove such relationships is by constructing 
 an Euler System (ES). An Euler System is a collection of Galois cohomology
  classes over ramified abelian extensions of the base field that verify so
 me co-restriction compatibilities. The key feature of ESs is that they pro
 vide a way to bound Selmer groups\, thanks to the machinery developed by R
 ubin\, inspired by earlier work of Thaine\, Kolyvagin\, and Kato. In this 
 talk\, I will present joint work with C. Skinner\, in which we develop a n
 ew method for constructing Euler Systems and apply it to build an ES for t
 he Galois representation attached to the symmetric square of an elliptic m
 odular form. I will stress how this method gives a unifying approach to co
 nstructing ESs\, in that it can be successfully applied to retrieve most c
 lassical ESs (the cyclotomic units ES\, the elliptic units ES\, Kato’s E
 S…).\n\n\n\n\n\n\n
CATEGORIES:Séminaire,Représentations des Groupes Réductifs
LOCATION:I2M Luminy - TPR2\, Salle de Séminaire 304-306 (3ème étage)\, 1
 63 Avenue de Luminy\, Marseille\, 13009\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, Mars
 eille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=I2M Luminy - TPR2\, Sall
 e de Séminaire 304-306 (3ème étage):geo:0,0
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DTSTART:20241027T020000
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