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The Kähler identity for bigraded Hodge-Lefschetz modules and its application in non-archimedean Arakelov geometry. (English) Zbl 0954.14017

Summary: We prove a Kähler identity for bigraded Hodge-Lefschetz modules and discuss its applications in non-archimedean Arakelov geometry. We consider, in particular, the bigraded Hodge-Lefschetz modules associated by Bloch, Gillet, and Soulé with a principal divisor with strict normal crossings on a scheme. The Kähler identity is used to prove a refined analogue of the \(dd^c\)-lemma for differential forms for these bigraded Hodge-Lefschetz modules. We apply this refined non-archimedean \(dd^c\)-lemma to investigate the arithmetic intersection pairing between cycles supported on the special fibers of semi-stable models of curves and abelian varieties.

MSC:

14G40 Arithmetic varieties and schemes; Arakelov theory; heights
14G20 Local ground fields in algebraic geometry
32K15 Differentiable functions on analytic spaces, differentiable spaces
14C15 (Equivariant) Chow groups and rings; motives
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
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