Abstract
Let G be an algebraic, connected, reductive group over a global field F of characteristic zero. We introduce a notion of vanishing family of compact subgroups K of G over the finite adeles and use it to compute asymptotically Lefschetz numbers and (at least conjecturally) the number of points of Shimura varieties (attached to G and K) over finite fields. We deduce a general setting giving families of Shimura curves reaching the Drinfeld–Vlăduţ bound. To cite this article: F. Sauvageot, C. R. Acad. Sci. Paris, Ser. I 342 (2006).
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