Multi angle Local densities compute isogeny classes
Auteurs : Achter, Jeffrey (Auteur de la Conférence)
CIRM (Editeur )
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Résumé : Consider an ordinary isogeny class of elliptic curves over a finite, prime field. Inspired by a random matrix heuristic (which is so strong it's false), Gekeler defines a local factor for each rational prime. Using the analytic class number formula, he shows that the associated infinite product computes the size of the isogeny class.Codes MSC :
I'll explain a transparent proof of this formula; it turns out that this product actually computes an adelic orbital integral which visibly counts the desired cardinality. Moreover, the new perspective allows a natural generalization to higher-dimensional abelian varieties. This is joint work with Julia Gordon and S. Ali Altug.
11G20 - Curves over finite and local fields
14G15 - Finite ground fields
22E35 - Analysis on $p$-adic Lie groups
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