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Isocrystals with additional structure. II. (English) Zbl 0966.20022
Summary: Let \(F\) be a \(p\)-adic field, let \(L\) be the completion of a maximal unramified extension of \(F\), and let \(\sigma\) be the Frobenius automorphism of \(L\) over \(F\). For any connected reductive group \(G\) over \(F\) one denotes by \(B(G)\) the set of \(\sigma\)-conjugacy classes in \(G(L)\) (elements \(x,y\) in \(G(L)\) are said to be \(\sigma\)-conjugate if there exists \(g\) in \(G(L)\) such that \(g^{-1} \kappa\sigma (g)=y)\). One of the main results of this paper is a concrete description of the set \(B(G)\) (previously this was known only in the quasi-split case [cf. Part I, ibid. 56, 201-220 (1985; Zbl 0597.20038)]).

MSC:
20G25 Linear algebraic groups over local fields and their integers
14F30 \(p\)-adic cohomology, crystalline cohomology
11S25 Galois cohomology
14L05 Formal groups, \(p\)-divisible groups
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