On multilinearity and skew-symmetry of certain symbols in motivic cohomology of fields
| dc.creator | Myung, Sung | |
| dc.date | 2008-01-09 | |
| dc.date | 2008-09-15 | |
| dc.date.accessioned | 2026-07-07T13:14:44Z | |
| dc.date.available | 2026-07-07T13:14:44Z | |
| dc.description | 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. | |
| dc.description | We acknowledge that mutilinearity does not hold for arbitrary symbols in H^{l-1} (Spec k, Z(l)) as claimed in the 1st version and this mistake has been corrected in the 2nd version | |
| dc.identifier | https://arxiv.org/abs/0801.1405 | |
| dc.identifier | http://arxiv.org/abs/0801.1405 | |
| dc.identifier | Math. Res. Lett. 16 (2009): 303-322 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230270 | |
| dc.subject | K-Theory and Homology | |
| dc.title | On multilinearity and skew-symmetry of certain symbols in motivic cohomology of fields | |
| dc.type | text |