论文标题
具有系数和特征多项式的Witt载体在非交通环上
Witt vectors with coefficients and characteristic polynomials over non-commutative rings
论文作者
论文摘要
对于不必要的交换环r，我们定义了一个在r型模块中具有系数的Abelian w（r; m）。这些群体概括了通常的通勤环的通常大型维特矢量，我们证明它们具有类似的形式和结构。一个主要结果是W（r）：= W（r; r）在R中不变。 对于有限生成的投影R模块的R线性内态f，我们在W（r）$中定义了一个特征元素$χ_f\。该元素是经典特征多项式的非共同类似物，我们表明它具有相似的属性。分配$ f \ mapstoχ_f$引起了适当完成环状K理论和W（r）之间的同构。
For a not-necessarily commutative ring R we define an abelian group W(R;M) of Witt vectors with coefficients in an R-bimodule M. These groups generalize the usual big Witt vectors of commutative rings and we prove that they have analogous formal properties and structure. One main result is that W(R) := W(R;R) is Morita invariant in R. For an R-linear endomorphism f of a finitely generated projective R-module we define a characteristic element $χ_f \in W(R)$. This element is a non-commutative analogue of the classical characteristic polynomial and we show that it has similar properties. The assignment $f \mapsto χ_f$ induces an isomorphism between a suitable completion of cyclic K-theory and W(R).
