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SUMMARY:Melanie Wood (Harvard)
DTSTART:20211118T223000Z
DTEND:20211118T233000Z
DTSTAMP:20260423T040709Z
UID:JNTS/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/JNTS/30/">Th
 e average size of 3-torsion in class groups of 2-extensions</a>\nby Melani
 e Wood (Harvard) as part of Columbia CUNY NYU number theory seminar\n\n\nA
 bstract\nThe $p$-torsion in the class group of a number field $K$ is conje
 ctured to\nbe small: of size at most $|\\text{Disc}\\\,K |^\\epsilon$\, an
 d to have constant\naverage size in families with a given Galois closure g
 roup (when $p$\ndoesn't divide the order of the group).  In general\, the 
 best upper\nbound we have is $|\\text{Disc}\\\, K|^{1/2+\\epsilon}$\, and 
 previously the only two\ncases known with constant average were for 3-tors
 ion in quadratic\nfields (Davenport and Heilbronn\, 1971) and 2-torsion in
  non-Galois\ncubic fields (Bhargava\, 2005).  We prove that the 3-torsion 
 is\nconstant on average for fields with Galois closure group any 2-group\n
 with a transposition\, including\, e.g. quartic $D_4$ fields.  We will\ndi
 scuss the main inputs into the proof with an eye towards giving an\nintrod
 uction to the tools in the area.  This is joint work with Robert\nLemke Ol
 iver and Jiuya Wang.\n
LOCATION:https://researchseminars.org/talk/JNTS/30/
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