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SUMMARY:Waqar Ali Shah (Bilkent University)
DTSTART:20260408T160000Z
DTEND:20260408T170000Z
DTSTAMP:20260422T102035Z
UID:FGC-IPM/67
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FGC-IPM/67/"
 >An introduction to Euler systems</a>\nby Waqar Ali Shah (Bilkent Universi
 ty) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nThe Birch
 –Swinnerton-Dyer conjecture and its generalization\,\nthe Bloch–Kato c
 onjecture\, predict a deep relationship between special\nvalues of $L$-fun
 ctions and arithmetic invariants such as Selmer groups.\nOne of the most p
 owerful tools for studying these conjectures is the\ntheory of Euler syste
 ms\, which provides a mechanism for bounding Selmer\ngroups using compatib
 le families of cohomology classes. In this talk\, I\nwill give an introduc
 tion to the theory of Euler systems and explain how\nthey arise naturally 
 in the setting of automorphic forms and Shimura\nvarieties. I will then di
 scuss some new examples arising from unitary\nand Siegel Shimura varieties
 \, where new phenomena related to the\nnon-uniqueness of period integrals 
 appear\, and outline recent ideas for\novercoming these difficulties in th
 e construction of Euler systems.\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/67/
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