https://hal-ens-lyon.archives-ouvertes.fr/ensl-01420357Niziol, WieslawaWieslawaNiziolENS Lyon - École normale supérieure - LyonOn syntomic regukators I: constructions.HAL CCSD2016[MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT][MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]niziol, wieslawa2016-12-20 14:47:202019-11-19 10:34:352016-12-21 10:02:32enPreprints, Working Papers, ...application/pdf1We 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].