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On syntomic regukators I: constructions.

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Wieslawa Niziol
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Abstract

We show that classical Chern classes from higher (p-adic) K-theory to syntomic cohomology extend to logarithmic syntomic cohomology. These Chern classes are compatible – in a suitable sense – with addition, products, and λ-operations. They are also compatible with the canonical Gysin sequences and, via period maps, with logarithmicétalelogarithmicétale Chern classes. Moreover, they induce logarithmic crystalline Chern classes. This uses as a critical new ingredient the recent comparison of syntomic cohomology with p-adic nearby cycles [6] and p-adic motivic cohomology [7].
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ensl-01420357 , version 1 (20-12-2016)

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  • HAL Id : ensl-01420357 , version 1

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Wieslawa Niziol. On syntomic regukators I: constructions.. 2016. ⟨ensl-01420357⟩

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