关于域的动机上同调中某些符号的多重线性和斜对称性
On multilinearity and skew-symmetry of certain symbols in motivic cohomology of fields
摘要：
本文的目的是在两种情况下证明Goodwillie-Lichtenbaum复形中符号的多重线性。第一种情况是度等于权重。在这种情况下，一个域的motivic上同调群同构于Milnor的K-群，如Nesterenko-Suslin，Totaro和Suslin-Voevodsky对各种motivic复形所示，但我们给出了Goodwillie-Lichtenbaum复形的显式同构，其形式明显地将Milnor符号的多重线性带到我们的motivic符号的多重线性。其次，我们建立了H^{l-1}（Spec k，Z（l））中不可约Goodwillie-Lichtenbaum符号的多重线性和斜对称性。这些性质已预计举行从作者的建设双线性型的双对数的情况下k是一个子域的领域的复数和l=2。其次，我们建立了H^{l-1}（Spec k，Z（l））中Goodwillie-Lichtenbaum符号的多重线性和斜对称性。这些性质已预计举行从作者的建设双线性型的双对数的情况下k是一个子域的领域的复数和l=2。符号的多重线性可以被看作是众所周知的公式det（AB）= det（A）det（B）对于交换矩阵元组的推广。
英文摘要：
The purpose of the present article is to show the multilinearity for symbols in Goodwillie-Lichtenbaum complex in two cases. The first case shown is where the degree is equal to the weight. In this case, the motivic cohomology groups of a field are isomorphic to the Milnor's K-groups as shown by Nesterenko-Suslin, Totaro and Suslin-Voevodsky for various motivic complexes, but we give an explicit isomorphism for Goodwillie-Lichtenbaum complex in a form which visibly carries multilinearity of Milnor's symbols to our multilinearity of motivic symbols. Next, we establish multilinearity and skew-symmetry for irreducible Goodwillie-Lichtenbaum symbols in H^{l-1} (Spec k, Z(l)). These properties have been expected to hold from the author's construction of a bilinear form of dilogarithm in case k is a subfield of the field of complex numbers and l=2. Next, we establish multilinearity and skew-symmetry for Goodwillie-Lichtenbaum symbols in H^{l-1} (Spec k, Z(l)). These properties have been expected to hold from the author's construction of a bilinear form of dilogarithm in case k is a subfield of the field of complex numbers and l=2. The multilinearity of symbols may be viewed as a generalization of the well-known formula det(AB) = det(A) det(B) for tuples of commuting matrices.
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