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SUMMARY:Jiuya Wang (Duke University)
DTSTART:20210212T230000Z
DTEND:20210213T000000Z
DTSTAMP:20260423T024737Z
UID:UCSBsga/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSBsga/11/"
 >Pointwise Bound for $\\ell$-torsion of Class Groups</a>\nby Jiuya Wang (D
 uke University) as part of UCSB Seminar on Geometry and Arithmetic\n\n\nAb
 stract\n$\\ell$-torsion conjecture states that $\\ell$-torsion of the clas
 s group $|\\text{Cl}_K[\\ell]|$ for every number field $K$ is bounded by $
 \\text{Disc}(K)^{\\epsilon}$. It follows from a classical result of Brauer
 -Siegel\, or even earlier result of Minkowski that the class number $|\\te
 xt{Cl}_K|$ of a number field $K$ are always bounded by $\\text{Disc}(K)^{1
 /2+\\epsilon}$\, therefore we obtain a trivial bound\n$\\text{Disc}(K)^{1/
 2+\\epsilon}$ on $|\\text{Cl}_K[\\ell]|$. We will talk about recent works 
 on breaking the trivial bound for $\\ell$-torsion of class groups in some 
 cases based on the work of Ellenberg-Venkatesh. We will also mention sever
 al questions following this line.\n
LOCATION:https://researchseminars.org/talk/UCSBsga/11/
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