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SUMMARY:Pip Goodman
DTSTART:20210609T150000Z
DTEND:20210609T160000Z
DTSTAMP:20260418T065335Z
UID:LNTS/41
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/41/">Su
 perelliptic curves with large Galois images</a>\nby Pip Goodman as part of
  London number theory seminar\n\n\nAbstract\nLet $K$ be a number field. Th
 e inverse Galois problem for $K$ asks if for every finite group $G$ there 
 exists a Galois extension $L/K$ whose Galois group is isomorphic to $G$. M
 any people have used torsion points on abelian varieties to realise symple
 ctic similitude groups (${\\rm GSp}_n(F_\\ell)$) over $Q$.\n\nIn this talk
 \, we examine mod $\\ell$ Galois representations attached to superelliptic
  curves and use them to realise general linear and unitary similitude grou
 ps over cyclotomic fields. A variety of mathematics is involved\, includin
 g group theory\, CM theory\, root discriminant bounds\, and models of curv
 es.\n
LOCATION:https://researchseminars.org/talk/LNTS/41/
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