\(p\)-adic cocycles and their regulator maps. (English) Zbl 1232.19004
The authors derive a power series formula for the \(p\)-adic regulator on the higher dimensional algebraic \(K\)-groups of number fields. This formula is designed to be well suited to computer calculations and to reduction modulo powers of \(p\).
Reviewer: Tong Wenting (Nanjing)
MSC:
| 19F27 | Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects) |
| 14F20 | Étale and other Grothendieck topologies and (co)homologies |
| 14G20 | Local ground fields in algebraic geometry |
| 11F70 | Representation-theoretic methods; automorphic representations over local and global fields |
References:
| [1] | DOI: 10.1016/j.crma.2006.02.039 · Zbl 1104.19005 · doi:10.1016/j.crma.2006.02.039 |
| [2] | DOI: 10.1016/S0764-4442(00)00154-3 · Zbl 0947.19003 · doi:10.1016/S0764-4442(00)00154-3 |
| [3] | Burgos Gil, Centre de Récherches Mathématiques Monograph Sér. 15 (2002) |
| [4] | Wagoner, Springer-Verlag Lecture Notes in Mathematics 551 pp 241– (1976) |
| [5] | Soulé, Springer-Verlag Lecture Notes in Mathematics 854 pp 372– (1981) |
| [6] | Karoubi, C.R. Acad. Sci. Paris Sr. I Math. 297 pp 557– (1983) |
| [7] | Snaith, Cambridge Studies in Advanced Math. 40 (1994) |
| [8] | Nesterenko, (Russian) Izv. Akad. Nauk. SSSR Ser. Mat. 53 pp 121– (1989) |
| [9] | Lazard, Pub. Math. I.H.E.S. 26 pp 389– (1965) |
| [10] | Karoubi, Astérisque 149 (1987) |
| [11] | Snaith, Fields Institute Communications Series 16 pp 285– (1997) |
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