\(K\)-groups of reciprocity functors for \(\mathbb{G}_a\) and abelian varieties. (English) Zbl 1326.19002
The authors set out to prove a result they describe as follows: “We prove that the \(K\)-group of reciprocity functors, defined by F. Ivorra and the first author [“\(K\)-groups of reciprocity functors”, arxiv:1209.1217], vanishes over a perfect field as soon as one of the reciprocity functors is \(\mathbb{G}_a\) and one is an abelian variety”. They do so in an expeditious and unadorned fashion. As they point out, in the case of characteristic zero this establishes a conjecture of B. Kahn [“Foncteurs de Mackey à réciprocité”, Preprint, arXiv:1210.7577].
Reviewer: Tom Bachmann (München)
MSC:
| 19E15 | Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects) |
| 19D45 | Higher symbols, Milnor \(K\)-theory |
| 14F42 | Motivic cohomology; motivic homotopy theory |
| 19F15 | Symbols and arithmetic (\(K\)-theoretic aspects) |
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