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SUMMARY:Debanjana Kundu (University of Regina)
DTSTART:20260413T190000Z
DTEND:20260413T200000Z
DTSTAMP:20260423T022228Z
UID:ANTS/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ANTS/22/">On
  the $p$-ranks of class groups of certain Galois extensions</a>\nby Debanj
 ana Kundu (University of Regina) as part of Calgary Algebra and Number The
 ory Seminar\n\nLecture held in MS 337.\n\nAbstract\nLet $p$ be an odd prim
 e\, let $N$ be a prime with $N \\equiv 1 \\pmod{p}$\, and let $\\zeta_p$ b
 e a primitive $p$-th root of unity. We study the $p$-rank of the class gro
 up of $\\mathbb{Q}(\\zeta_p\, N^{1/p})$ using Galois cohomological methods
  and obtain an exact formula for the $p$-rank in terms of the dimensions o
 f certain Selmer groups. Using our formula\, we provide a numerical criter
 ion to establish upper and lower bounds for the $p$-rank\, analogous to th
 e numerical criteria provided by F.~Calegari--M.~Emerton and K.~Schaefer--
 E.~Stubley for the $p$-ranks of the class group of $\\mathbb{Q}(N^{1/p})$.
  In the case $p=3$\, we use Redei matrices to provide a numerical criterio
 n to exactly calculate the $3$-rank\, and also study the distribution of t
 he $3$-ranks as $N$ varies through primes which are $4\,7 \\pmod{9}$. This
  is joint work with Ufuoma Asenhesa\, Rusiru Gambheera\, Enrique Nunez Lon
 -Wo\, and Arshay Sheth.\n
LOCATION:https://researchseminars.org/talk/ANTS/22/
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