# On syntomic regulators I: constructions

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.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal-ens-lyon.archives-ouvertes.fr/ensl-01956991
Contributor : Wieslawa Niziol <>
Submitted on : Monday, December 17, 2018 - 5:00:41 AM
Last modification on : Tuesday, December 18, 2018 - 1:04:20 AM

### Identifiers

• HAL Id : ensl-01956991, version 1
• ARXIV : 1607.04975

### Citation

Wieslawa Niziol. On syntomic regulators I: constructions. 2018. ⟨ensl-01956991⟩

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