Séminaires : Séminaire Théorie des Nombres

Equipe(s) : tn,
Responsables :Ziyang Gao, Marc Hindry, Bruno Kahn, João Pedro P. dos Santos
Email des responsables : ziyang.gao@imj-prg.fr
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Orateur(s) A. Langer - ,
Titre On the bad reduction of Hirzebruch-Zagier curves
Date09/12/2002
Horaire14:00 à 16:00
Diffusion
RésumeWe consider the Tate-conjecture for divisors in finitecharacteristic for a certain class of Hilbert modular surfaceswhereall Hilbert modular forms are lifts of elliptic modular forms.If p splits in the underlying real quadratic field the Conjectureis shown by considering components in the reduction of a non-compactHirzebruch-Zagier curve(the image of a modular curve).If p is inert the whole cusidal cohomology is supposed to be coveredby cycle classes in char. p. We construct-for each isotypic componentunder the action of the Hecke-algebra- a new cycle class by consideringa Shimura curve having bad reduction at p, the components in the reductionly in the supersingular locus of the surface and give rise to new cycleclasses
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