THE COMPLEXITY OF HIGHER CHOW GROUPS

GENIVAL DA SILVA, JAMES D. LEWIS
2022 Canadian mathematical bulletin  
Let X/C be a smooth projective variety. We consider two integral invariants, one of which is the level of the Hodge cohomology algebra H * (X, C) and the other involving the complexity of the higher Chow groups CH * (X, m; Q) for m ≥ 0. We conjecture that these two invariants are the same and accordingly provide some strong evidence in support of this.
doi:10.4153/s0008439522000509 fatcat:vvidjinapfb5loqohlzvmov3hy