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\(p\)-adic automorphic forms on reductive groups. (English) Zbl 1122.11026
Tilouine, Jacques (ed.) et al., Formes automorphes (I). Actes du Semestre du Centre Émile Borel, Paris, France, 17 février au 11 juillet 2000. Paris: Société Mathématique de France (ISBN 2-85629-172-4/pbk). Astérisque 298, 147-254 (2005).
Let \(p\) be a prime number. The author presents in these lecture notes his theory of families of \(p\)-ordinary \(p\)-adic automorphic forms on reductive groups [see a.o. J. Inst. Math. Jussieu 1, No. 1, 1–76 (2002; Zbl 1039.11041), \(p\)-adic automorphic forms on Shimura varieties. New York, NY: Springer (2004; Zbl 1055.11032)]. The main themes are: Vertical Control Theorems about construction of \(p\)-adic families, \(p\)-adic \(L\)-functions in symplectic and unitary cases, Galois representations, the Iwasawa theoretic significance of \(p\)-adic \(L\)-functions.
For the entire collection see [Zbl 1063.11002].

MSC:
11F33 Congruences for modular and \(p\)-adic modular forms
11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
11F55 Other groups and their modular and automorphic forms (several variables)
11G18 Arithmetic aspects of modular and Shimura varieties
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