An additive version of higher Chow groups
| dc.creator | Bloch, Spencer | |
| dc.creator | Esnault, Hélène | |
| dc.date | 2001-12-11 | |
| dc.date.accessioned | 2026-07-07T04:45:10Z | |
| dc.date.available | 2026-07-07T04:45:10Z | |
| dc.description | The cosimplicial scheme $$Delta^bullet = Δ^0 smallmatrix \to smallmatrix Δ^1 smallmatrix to smallmatrix ...;\quad Δ^n :=\Spec\Big(k[t_0,...c,t_n]/(\sum t_i -t)\Big)$$ was used in B to define higher Chow groups. In this note, we let t tend to 0 and replace Δ^\bullet by a degenerate version $$Q^\bullet = Q^0 smallmatrix to smallmatrix Q^1 smallmatrix to smallmatrix ...;\quad Q^n := \Spec\Big(k[t_0,...c,t_n]/(\sum t_i)\Big) $$ to define an additive version of the higher Chow groups. For a field k, we show the Chow group of 0-cycles on $Q^n$ in this theory is isomorphic to the absolute $(n-1)$-Kähler forms $Ω^{n-1}_k$. An analogous degeneration on the level of de Rham cohomology associated to ``constant modulus'' degenerations of varieties in various contexts is discussed. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0112101 | |
| dc.identifier | http://arxiv.org/abs/math/0112101 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62862 | |
| dc.subject | Algebraic Geometry | |
| dc.title | An additive version of higher Chow groups | |
| dc.type | text |