Geodesic
The complexity of higher Chow groups
Canadian mathematical bulletin, Tome 66 (2023) no. 3, pp. 903-911

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DOI

Let $X/{\mathbb C}$ be a smooth projective variety. We consider two integral invariants, one of which is the level of the Hodge cohomology algebra $H^*(X,{\mathbb C})$ and the other involving the complexity of the higher Chow groups ${\mathrm {CH}}^*(X,m;{\mathbb Q})$ for $m\geq 0$. We conjecture that these two invariants are the same and accordingly provide some strong evidence in support of this.
DOI : 10.4153/S0008439522000509
Mots-clés : Higher Chow groups, Bloch–Beilinson filtration, Hodge conjecture, Abel–Jacobi map 
Jr, Genival Da Silva; Lewis, James D. The complexity of higher Chow groups. Canadian mathematical bulletin, Tome 66 (2023) no. 3, pp. 903-911. doi: 10.4153/S0008439522000509
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     title = {The complexity of higher {Chow} groups},
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     year = {2023},
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