Geodesic
A Cycle Class Map from Chow Groups with Modulus to Relative $K$-Theory
Documenta mathematica, Tome 23 (2018), pp. 407-444

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Let X be a smooth quasi-projective d-dimensional variety over a field k and let D be an effective, non-reduced, Cartier divisor on it such that its support is strict normal crossing. In this note, we construct cycle class maps from (a variant of) the higher Chow group with modulus of the pair (X;D) in the range (d+n,n) to the relative K-groups Kn​(X;D) for every n≥0.
DOI : 10.4171/dm/623
Classification : 14C25, 14F42, 19E15
Mots-clés : cycles with modulus, relative K-theory, cycle class map, non-A1-invariant motives 
Federico Binda. A Cycle Class Map from Chow Groups with Modulus to Relative $K$-Theory. Documenta mathematica, Tome 23 (2018), pp. 407-444. doi: 10.4171/dm/623
@article{10_4171_dm_623,
     author = {Federico Binda},
     title = {A {Cycle} {Class} {Map} from {Chow} {Groups} with {Modulus} to {Relative} $K${-Theory}},
     journal = {Documenta mathematica},
     pages = {407--444},
     year = {2018},
     volume = {23},
     doi = {10.4171/dm/623},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/623/}
}
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