Cycle class maps for Chow groups of zero-cycles with modulus
نویسندگان
چکیده
For a smooth scheme X of pure dimension d over field k and an effective Cartier divisor D?X whose support is simple normal crossing divisor, we construct cycle class mapcycX|D:CH0(X|D)?HNisd(X,KdM(OX,ID)) from the Chow group zero-cycles with modulus to cohomology relative Milnor K-sheaf.
منابع مشابه
Chow groups of Zero-Cycles Relative to Hyperplane Arrangements
The schemes Spec (k[x0, . . . , xn]/( P xi − 1)) were used homologically by Bloch to define higher Chow groups. We prove an alternate, ‘classical’, characterization of higher Chow groups, in the zero-cycle case over a field k, in terms of divisors of functions on curves. Since an arrangement of hyperplanes A is given by a finite number of linear forms on affine space, such as the n + 1 forms xi...
متن کاملAlgebraic Cycles and Additive Chow Groups
A report on recent results and outstanding problems concerning additive chow groups. “Mighty oaks from little acorns grow.”
متن کاملAdditive Chow Groups with Higher Modulus and the Generalized De Rham-witt Complex
Bloch and Esnault defined additive higher Chow groups with modulus (m + 1) on the level of zero cycles over a field k, denoted by TH(k, n;m), n, m ≥ 1. They prove TH(k, n; 1) ∼= Ω k/Z . In this paper we generalize their result and obtain an isomorphism TH(k, n;m) ∼= WmΩ n−1 k , where W−Ω·k is the generalized de Rham-Witt complex of Hesselholt-Madsen, generalizing the p-typical de Rham-Witt comp...
متن کاملChow Groups, Chow Cohomology, and Linear Varieties
We compute the Chow groups and Fulton–MacPherson’s operational Chow cohomology ring for a class of singular rational varieties including toric varieties. The computation is closely related to the weight filtration on the ordinary cohomology of these varieties. We use the computation to answer one of the open problems about operational Chow cohomology: it does not have a natural map to ordinary ...
متن کاملRelative cycles and Chow sheaves
3 Relative cycles. 15 3.1 Relative cycles. . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2 Cycles associated with flat subschemes. . . . . . . . . . . . . . 20 3.3 Chow presheaves. . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.4 Relative cycles over geometrically unibranch schemes. . . . . . 32 3.5 Multiplicities of components of inverse images of equidimensional cycles over...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2023
ISSN: ['1873-1376', '0022-4049']
DOI: https://doi.org/10.1016/j.jpaa.2022.107282