An additive version of higher Chow groups

By Spencer Bloch, H. Esnault. 2001

69 citations recorded by the source corpus.

Abstract The cosimplicial scheme Δ • = Δ 0 → → Δ 1 → → → …; Δ n := Spec k[t 0 ,…,t n ]/ ∑t i −t was used in (Bloch, S., Algebraic cycles and higher K-theory, Adv. Math. 61 (3) (1986) 267–304) to define higher Chow groups. In this note, we let t tend to 0 and replace Δ• by a degenerate version Q • =Q 0 → → Q 1 → → → …;Q n := Spec k[t 0 ,…,t n ]/ ∑t i to define an additive version of the higher Chow groups. For a field k, we show the Chow group of 0-cycles on Qn in this theory is isomorphic to the group of absolute (n−1)-Kahler 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.

Subfields: Geometry and Topology, Mathematical Physics, Pharmacology

View Paper: https://www.semanticscholar.org/paper/b65ba4bc22501b488643be6d753a03ad82ffe183

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In Geometry and Topology

1. S. Saito
2. F. Binda
3. H. Esnault
4. Spencer Bloch
5. Carlos Simpson
6. C. Sabbah
7. O. Fujino
8. L. Illusie

In Mathematical Physics

1. S. Saito
2. F. Binda
3. H. Esnault
4. Spencer Bloch
5. Carlos Simpson
6. C. Sabbah
7. M. Kerr
8. Minhyong Kim

In Pharmacology

1. F. Binda
2. S. Saito
3. H. Esnault
4. Spencer Bloch

Citations in the corpus

• The additive dilogarithm (2002, methodology): “One first applies a Bertini type argument as in [6], Proposition 4.”
• RELATIVE CYCLES WITH MODULI AND REGULATOR MAPS (2014, methodology): “(2) The above definition generalizes the additive higher Chow groups defined by Bloch and Esnault [2], Park [35], Krishna and Levine [25].”