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SUMMARY:Douglas Ulmer (University of Arizona)
DTSTART:20230327T180000Z
DTEND:20230327T190000Z
DTSTAMP:20260423T021137Z
UID:NTC/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTC/10/">$p$
 -torsion of Jacobians for unramified $\\mathbb{Z}/p\\mathbb{Z}$-covers of 
 curves</a>\nby Douglas Ulmer (University of Arizona) as part of Lethbridge
  number theory and combinatorics seminar\n\nLecture held in University of 
 Lethbridge: M1040 (Markin Hall).\n\nAbstract\nIt is a classical problem to
  understand the set of Jacobians of curves\namong all abelian varieties\, 
 i.e.\, the image of the map $M_g\\to A_g$\nwhich sends a curve $X$ to its 
 Jacobian $J_X$.  In characteristic $p$\,\n$A_g$ has interesting filtration
 s\, and we can ask how the image of\n$M_g$ interacts with them.  Concretel
 y\, which groups schemes arise as\nthe p-torsion subgroup $J_X[p]$ of a Ja
 cobian?  We consider this\nproblem in the context of unramified $Z/pZ$ cov
 ers $Y\\to X$ of curves\,\nasking how $J_Y[p]$ is related to $J_X[p]$.  Tr
 anslating this into a\nproblem about de Rham cohmology yields some results
  using\nclassical ideas of Chevalley and Weil.  This is joint work with Br
 yden\nCais.\n
LOCATION:https://researchseminars.org/talk/NTC/10/
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