To the multidimensional tame symbol
Abstrak
We give a construction of the two-dimensional tame symbol as the commutator of a group-like monoidal groupoid which is obtained from some group of k-linear operators acting in a two-dimensional local field and corresponds to some third cohomology class of this group. We give also the hypothetical method for the proof of the two-dimensional Parshin reciprocity laws. This text was written in 2003 as preprint 03-13 of the Humboldt University of Berlin and was available at this http URL (only evident misprints are corrected now). Later E. Frenkel and X. Zhu obtained in arXiv:0810.1487 [math.RT] more general results concerning the third cohomology classes of groups acting on two-dimensional local fields, and the author and X. Zhu obtained in arXiv:1002.4848 [math.AG] the proof of the Parshin reciprocity laws on an algebraic surface similar to the Tate proof of the residue formula on an algebraic curve.
Topik & Kata Kunci
Penulis (1)
D. Osipov
Akses Cepat
- Tahun Terbit
- 2003
- Bahasa
- en
- Total Sitasi
- 5×
- Sumber Database
- Semantic Scholar
- DOI
- 10.18452/2609
- Akses
- Open Access ✓