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SUMMARY:Christophe Ritzenthaler (Rennes)
DTSTART:20200514T170000Z
DTEND:20200514T180000Z
DTSTAMP:20260422T053420Z
UID:SFUQNTAG/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SFUQNTAG/2/"
 >Jacobians in the isogeny class of E^g</a>\nby Christophe Ritzenthaler (Re
 nnes) as part of SFU NT-AG seminar\n\n\nAbstract\nLet $E$ be an ordinary e
 lliptic curve over a finite field $\\mathbb{F}_q$ such that $R=\\mathrm{En
 d}(E)$ is generated by the Frobenius endomorphism. There is an equivalence
  of categories which associates to each abelian variety $A$ in the isogeny
  class of $E^g$ an $R$-lattice $L$ of rank $g$.  Given $L$ (with a hermiti
 an form describing a polarization $a$ on $A$)\, we show how to make $(A\,a
 )$ concrete\, i.e. we give an embedding of $(A\,a)$ into a projective spac
 e by computing its algebraic theta constants. Using these data and an algo
 rithm to compute Siegel modular forms algebraically\, we can decide when $
 (A\,a)$ is a Jacobian over $\\mathbb{F}_q$ when $g \\leq 3$ (and over $\\b
 ar{\\mathbb{F}}_q$ when $g=4$). We illustrate our algorithms with the prob
 lem of constructing curves over $\\mathbb{F}_q$ with many rational points.
 \n<p>Joint work with Markus Kirschmer\, Fabien Narbonne and Damien Robert<
 /p>\n
LOCATION:https://researchseminars.org/talk/SFUQNTAG/2/
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