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SUMMARY:On the conversion of module representations for higher dimensional
  supersingular isogenies
DTSTART:20260611T120000Z
DTEND:20260611T170000Z
DTSTAMP:20260616T052400Z
UID:indico-event-16283@indico.math.cnrs.fr
DESCRIPTION:Speakers: Julien Soumier\n\nThe Deuring correspondence between
  supersingular ellipticcurves and quaternionic ideals is a major tool to d
 esign efficientalgorithms for working with one dimensional abelian varieti
 es of knownendomorphism ring. The module correspondence can be seen as a n
 ewframework extending this correspondence in higher dimension. It isruled 
 by the same idea that\, given some extra information aboutmorphisms from a
 n abelian variety\, we can reduce hard problems tolinear algebra over a no
 n commutative ring.\nIn this talk we present our results from a joint work
  with Aurel Pageand Damien Robert. After recalling the basis of the module
 correspondence\, we will describe our solution to the Principal IdealProbl
 em in matrix spaces over quaternionic orders\, along with analgorithm that
  computes the principally polarized abelian varietyassociated with an Herm
 itian module. We will also highlight that thesealgorithms enable the compu
 tation of unpolarized isomorphisms betweenmaximal abelian varieties\, give
 n their module representation.\n\nhttps://indico.math.cnrs.fr/event/16283/
URL:https://indico.math.cnrs.fr/event/16283/
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