\(p\)-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) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.