Isogeny Classes of Hilbert–Blumenthal Abelian Varieties over Finite Fields
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In this paper, the authors give an explicit formula for the size of the isogeny class of a Hilbert-Blumenthal abelian variety over a finite field, where OL is the ring of integers in a totally real field dimension g over Q, N 0 and N N 0 are relatively prime square-free integers, and k is a relatively prime field of characteristic relatively prime to both N 0N and disc(L, Q).About:
This article is published in Journal of Number Theory.The article was published on 2002-02-01 and is currently open access. It has received 3 citations till now. The article focuses on the topics: Isogeny & Abelian group.read more
Citations
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Otto Blumenthal (1876-1944) in retrospect
Paul L. Butzer,Lutz Volkmann +1 more
TL;DR: The life and work of Otto Blumenthal, one of the most tragic figures of the 188 emigre mathematicians from Germany and the Nazi-occupied continent, is treated in detail.
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Elliptic curves, random matrices and orbital integrals
TL;DR: In this article, the authors give a new, transparent proof of this formula; it turns out that this product actually computes an adelic orbital integral which visibly counts the desired cardinality.
Journal ArticleDOI
Elliptic curves, random matrices and orbital integrals
Jeffrey D. Achter,Julia Gordon +1 more
TL;DR: It turns out that this product actually computes an adelic orbital integral which visibly counts the desired cardinality, which answers a question posed by N. Katz.
References
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Journal ArticleDOI
Endomorphisms of Abelian Varieties over Finite Fields.
TL;DR: In this paper, it was shown that HOmk(A', A") is a free module of rank 2g over the ring Z l of l-adic integers, and the canonical map is Z-free.
Book
Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120), Volume 120
James Arthur,Laurent Clozel +1 more
TL;DR: In this article, the base change problem for arithmetic subgroups of GL(n,E) and GL (n,F) is studied, where E/F is a cyclic extension of number fields.
Journal ArticleDOI
Points on some Shimura varieties over finite fields
TL;DR: In this article, the Eichler-Shimura congruence relation was used to make the connection between the Hasse-Weil zeta function and automorphic L-functions.
Book
Base change for gl(2)
TL;DR: Langlands as discussed by the authors showed that it is possible to transfer automorphic representations of GL(2) over one number field to representations over a cyclic extension of the field.
Journal ArticleDOI
Theory of spherical functions on reductive algebraic groups over p-adic fields
TL;DR: In this paper, the authors present conditions générales d'utilisation (http://www.numdam.org/conditions), i.e., Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.