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

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Let $\overline{X}$ 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 $(\overline{X};D)$ in the range $(d+n, n)$ to the relative $K$-groups $K_n(\overline{X}; D)$ for every $n\geq 0$.
Classification : 14C25, 19E15, 14F42
Keywords: cycles with modulus, relative $K$-theory, cycle class map, non-$\mathbb{A}^1$-invariant motives 
@article{DOCMA_2018__23__a49,
     author = {Binda, Federico},
     title = {A {Cycle} {Class} {Map} from {Chow} {Groups} with {Modulus} to {Relative} $K${-Theory}},
     journal = {Documenta mathematica},
     pages = {407--444},
     publisher = {mathdoc},
     volume = {23},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a49/}
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Binda, Federico. A Cycle Class Map from Chow Groups with Modulus to Relative $K$-Theory. Documenta mathematica, Tome 23 (2018), pp. 407-444. http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a49/