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SUMMARY:Jiuya Wang (Duke)
DTSTART:20200702T173000Z
DTEND:20200702T183000Z
DTSTAMP:20260423T004137Z
UID:MAGIC/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MAGIC/9/">Po
 intwise Bound for $\\ell$-torsion of Class Groups</a>\nby Jiuya Wang (Duke
 ) as part of MAGIC (Michigan - Arithmetic Geometry Initiative - Columbia)\
 n\n\nAbstract\n$\\ell$-torsion conjecture states that $\\ell$-torsion of t
 he class group $|\\text{Cl}_K[\\ell]|$ for every number field $K$ is bound
 ed by $\\text{Disc}(K)^{\\epsilon}$. It follows from a classical result of
  Brauer-Siegel\, or even earlier result of Minkowski that the class number
  $|\\text{Cl}_K|$ of a number field $K$ are always bounded by $\\text{Disc
 }(K)^{1/2+\\epsilon}$\, therefore we obtain a trivial bound $\\text{Disc}(
 K)^{1/2+\\epsilon}$ on $|\\text{Cl}_K[\\ell]|$. We will talk about results
  on this conjecture\, and recent works on breaking the trivial bound for $
 \\ell$-torsion of class groups in some cases based on the work of Ellenber
 g-Venkatesh.\n
LOCATION:https://researchseminars.org/talk/MAGIC/9/
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