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Zbl 0716.11056
Gekeler, E.-U.
Sur la géométrie de certaines algèbres de quaternions. (On the geometry of certain quaternion algebras). (French)
[J] Sémin. Théor. Nombres Bordx., Sér. II 2, No.1, 143-153 (1990). ISSN 0989-5558

Let K be a global field; i.e., a number field or a function field in one variable over a finite field. Let D be an algebra of quaternions over K. Classically (i.e., over ${\bbfQ})$, one has a very lovely interpretation of concepts related to orders of D in terms of supersingular elliptic curves. In the paper under review the author carries out the same program in the function field case using supersingular Drinfeld modules of rank 2.
[D.Goss]

MSC 2000:: *11R52 Quaternion and other division algebras: arithmetic, zeta functions
11R58 Arithmetic theory of algebraic function fields
11G09 Drinfel'd modules, etc.
11G15 Complex multiplication and moduli of abelian varieties

Keywords: algebra of quaternions; orders; function field; supersingular Drinfeld modules

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