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- W4251010804 abstract "This chapter presents proofs of following theorems. Theorem 6.1: Suppose <italic>N</italic> in G<sub>arith</sub> is geometrically semisimple. Then G<sub>geom,N</sub> is a normal subgroup of <italic>Garith,N</italic>. Theorem 6.2: Suppose that <italic>N</italic> in G<sub>arith</sub> is arithmetically semisimple and pure of weight zero. If G<sub>arith,N</sub> is finite, then <italic>N</italic> is punctual. Indeed, if every Frobenius conjugacy class FrobE,X in G<sub>arith,N</sub> is quasiunipotent, then <italic>N</italic> is punctual. Theorem 6.4: Suppose that <italic>N</italic> in G<sub>arith</sub> is arithmetically semisimple and pure of weight zero. If G<sub>geom</sub> is finite, then <italic>N</italic> is punctual. Theorem 6.5: Suppose that <italic>N</italic> in G<sub>arith</sub> is arithmetically semisimple and pure of weight zero. Then the group G<sub>geom,N</sub>/G⁰<sub>geom,N</sub> of connected components of G<sub>geom,N</sub> is cyclic of some prime to <italic>p</italic> order <italic>n</italic>." @default.
- W4251010804 created "2022-05-12" @default.
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- W4251010804 date "2012-01-24" @default.
- W4251010804 modified "2023-09-24" @default.
- W4251010804 title "Group-Theoretic Facts about Ggeom and Garith" @default.
- W4251010804 doi "https://doi.org/10.23943/princeton/9780691153308.003.0007" @default.
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