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SUMMARY:Shiva Chidambaram (MIT)
DTSTART:20240228T200000Z
DTEND:20240228T210000Z
DTSTAMP:20261022T012617Z
UID:HarvardNT/104
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HarvardNT/10
 4/">Computing Galois images of Picard curves</a>\nby Shiva Chidambaram (MI
 T) as part of Harvard number theory seminar\n\nLecture held in Science Cen
 ter Room 507.\n\nAbstract\nLet $C$ be a genus $3$ curve whose Jacobian is 
 geometrically simple and has geometric endomorphism algebra equal to an im
 aginary quadratic field. In particular\, consider Picard curves $y^3 = f_4
 (x)$ where the geometric endomorphism algebra is $\\mathbb{Q}(\\zeta_3)$. 
 We study the associated mod-$\\ell$ Galois representations and their image
 s. I will discuss an algorithm\, developed in ongoing joint work with Pip 
 Goodman\, to compute the set of primes $\\ell$ for which the images are no
 t maximal. By running it on several datasets of Picard curves\, the larges
 t non-maximal prime we obtain is $13$. This may be compared with genus 1\,
  where Serre's uniformity question asks if the mod-$\\ell$ Galois image of
  non-CM elliptic curves over $\\Q$ is maximal for all primes $\\ell > 37$.
 \n
LOCATION:https://researchseminars.org/talk/HarvardNT/104/
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