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arXiv · 1607.04975

On syntomic regulators I: constructions

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 $\lambda$-operations. They are also compatible with the canonical Gysin sequences and, via period maps, with logarithmic \'etale 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 and $p$-adic motivic cohomology.

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Wieslawa Niziol. 2016-07-18. On syntomic regulators I: constructions. https://arxiv.org/abs/1607.04975

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