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SUMMARY:Jiuya Wang (Duke)
DTSTART:20210119T000000Z
DTEND:20210119T005000Z
DTSTAMP:20260423T041612Z
UID:UCLA_NTS/23
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCLA_NTS/23/
 ">Pointwise Bound for $\\ell$-torsion of Class Groups</a>\nby Jiuya Wang (
 Duke) as part of UCLA Number Theory Seminar\n\n\nAbstract\n$\\ell$-torsion
  conjecture states that $\\ell$-torsion of the\nclass group $|\\text{Cl}_K
 [\\ell]|$ for every number field $K$ is bounded\nby $\\text{Disc}(K)^{\\ep
 silon}$. It follows from a classical result of\nBrauer-Siegel\, or even ea
 rlier result of Minkowski that the class number\n$|\\text{Cl}_K|$ of a num
 ber field $K$ are always bounded by\n$\\text{Disc}(K)^{1/2+\\epsilon}$\, t
 herefore we obtain a trivial bound\n$\\text{Disc}(K)^{1/2+\\epsilon}$ on $
 |\\text{Cl}_K[\\ell]|$. We will talk\nabout results on this conjecture\, a
 nd recent works on breaking the\ntrivial bound for $\\ell$-torsion of clas
 s groups based on the work of\nEllenberg-Venkatesh.\n
LOCATION:https://researchseminars.org/talk/UCLA_NTS/23/
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