The Chow-Witt ring
نویسندگان
چکیده
منابع مشابه
Witt rings of quadratically presentable fields
This paper introduces an approach to the axiomatic theory of quadratic forms based on {tmem{presentable}} partially ordered sets, that is partially ordered sets subject to additional conditions which amount to a strong form of local presentability. It turns out that the classical notion of the Witt ring of symmetric bilinear forms over a field makes sense in the context of {tmem{quadratically p...
متن کاملHoles in I
Let F be a field with char(F ) 6= 2. We prove Vishik’s conjecture stating that for any positive integer n and any anisotropic quadratic form φ over F lying in the n-th power I of the fundamental ideal I of the Witt ring of F , either dim(φ) ≥ 2 or dim(φ) = 2 − 2 for some i ∈ {1, 2, . . . , n+ 1}. This provides a complete solution of an old-standing problem in the algebraic theory of quadratic f...
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 کاملOn Additive Higher Chow Groups of Affine Schemes
We show that the multivariate additive higher Chow groups of a smooth affine k-scheme Spec (R) essentially of finite type over a perfect field k of characteristic 6= 2 form a differential graded module over the big de Rham-Witt complex WmΩ • R. In the univariate case, we show that additive higher Chow groups of Spec (R) form a Witt-complex over R. We use these structures to prove an étale desce...
متن کاملStructure theorems for AP rings
In “New Proofs of the structure theorems for Witt Rings”, the first author shows how the standard ring-theoretic results on the Witt ring can be deduced in a quick and elementary way from the fact that the Witt ring of a field is integral and from the specific nature of the explicit annihilating polynomials he provides. We will show in the present article that the same structure results hold fo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006