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SUMMARY:Brody Lynch (UMass Amherst)
DTSTART:20260217T210000Z
DTEND:20260217T220000Z
DTSTAMP:20260422T173756Z
UID:FCNTS/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FCNTS/19/">E
 quidistribution of realizable Steinitz classes for Kummer extensions</a>\n
 by Brody Lynch (UMass Amherst) as part of Five College Number Theory Semin
 ar\n\nLecture held in Seeley Mudd 207 @Amherst College.\n\nAbstract\nLet $
 \\ell$ be prime\, and $K$ be a number field containing the $\\ell$-th root
 s of unity. We use techniques from classical algebraic number theory to pr
 ove that the Steinitz classes of $\\Z/\\ell\\Z$ extensions of $K$ are equi
 distributed among realizable classes in the ideal class group of $K$. Simi
 lar equidistribution results have been proved for Galois groups $S_2$ and 
 $S_3$ by Kable and Wright and $S_4$ and $S_5$ by Bhargava\, Shankar\, and 
 Wang using the theory of prehomogeneous vector spaces\, but this is the fi
 rst complete equidistribution result for an infinite class of Galois group
 s.\n\nNext\, we discuss generalizations of this result to elementary-$\\el
 l$ Galois groups using $V_4$ as an example. Additionally\, we will give so
 me initial results for Steinitz classes of ray class fields.\n
LOCATION:https://researchseminars.org/talk/FCNTS/19/
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