Degree one Milnor K-invariants of groups of multiplicative type
نویسندگان
چکیده
Let G be a commutative affine algebraic group over field F, and let H:FieldsF→AbGrps functor. A (homomorphic) H-invariant of is natural transformation Tors(−,G)→H, where Tors(−,G) the functor FieldsF→AbGrps taking extension L/F to isomorphism classes GL-torsors Spec(L). The goal this paper compute Invhom1(G,H) H-invariants when multiplicative type, H L×⊗ZQ/Z.
منابع مشابه
Class Groups of Multiplicative Invariants
Let G be a nite subgroup of GL d (Z). Then G acts on the Laurent polynomial ring kX 1 1 d ] over the eld k via the natural G-action on the multiplicative group generated by the variables X 1 ; : : : ; X d (= Z d). We show that the class group of the ring of invariants of this action is isomorphic to Hom(G=N;k) H 1 (G=D; (Z d) D), where N denotes the subgroup of G that is generated by all reeect...
متن کاملFinite Type Invariants and Milnor Invariants for Brunnian Links
A link L in the 3-sphere is called Brunnian if every proper sublink of L is trivial. In a previous paper, the first author proved that the restriction to Brunnian links of any Goussarov-Vassiliev finite type invariant of (n + 1)component links of degree < 2n is trivial. The purpose of this paper is to study the first nontrivial case. We show that the restriction of an invariant of degree 2n to ...
متن کاملA Regulator Formula for Milnor K-groups
The classical Abel–Jacobi map is used to geometrically motivate the construction of regulator maps from Milnor K-groups KM n (C(X)) to Deligne cohomology. These maps are given in terms of some new, explicit (n − 1)-currents, higher residues of which are defined and related to polylogarithms. We study their behavior in families Xs and prove a rigidity result for the regulator image of the Tame k...
متن کاملMilnor and Finite Type Invariants of Plat-closures
Finite type invariants of knots or links can be defined combinatorially using only link projections in S. In this setting it can be seen that every Jones-type polynomial invariant (quantum invariants) is equivalent to a sequence of finite type invariants. See [B2, BN] and references therein. Although Vassiliev’s original approach to finite type knot invariants ([V]) rests on topological foundat...
متن کاملMotivic interpretation of Milnor K-groups attached to Jacobian varieties
In the paper [Som90] p.105, Somekawa conjectures that his Milnor Kgroup K(k, G1, . . . , Gr) attached to semi-abelian varieties G1,. . . ,Gr over a field k is isomorphic to ExtrMk (Z, G1[−1] ⊗ . . . ⊗ Gr[−1]) where Mk is a certain category of motives over k. The purpose of this note is to give remarks on this conjecture, when we take Mk as Voevodsky’s category of motives DM (k) .
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 Algebra
سال: 2021
ISSN: ['1090-266X', '0021-8693']
DOI: https://doi.org/10.1016/j.jalgebra.2021.02.020