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- W4248315570 abstract "This chapter considers some arithmetic aspects of period maps with a geometric origin. It focuses on the situation Φ : <italic>S</italic>(ℂ) → Γ<italic>D</italic>, where <italic>S</italic> parametrizes a family <italic>X</italic> → <italic>S</italic> of smooth, projective varieties defined over a number field <italic>k</italic>. The chapter recalls the notion of absolute Hodge classes (AH) and strongly absolute Hodge classes (SAH). The particular case when the Noether-Lefschetz locus consists of isolated points is alluded to in the discussion of complex multiplication Hodge structures (CM Hodge structures). A related observation is that one may formulate a variant of the “Grothendieck conjecture” in the setting of period maps and period domains. The chapter also describes a behavior of fields of definition under the period map, along with the existence and density of CM points in a motivic variation of Hodge structure." @default.
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- W4248315570 date "2012-04-22" @default.
- W4248315570 modified "2023-09-28" @default.
- W4248315570 title "Arithmetic of Period Maps of Geometric Origin" @default.
- W4248315570 doi "https://doi.org/10.23943/princeton/9780691154244.003.0009" @default.
- W4248315570 hasPublicationYear "2012" @default.
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