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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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