A bound for the torsion in the \(K\)-theory of algebraic integers. (English) Zbl 1142.11375

Soulé, Christophe

Doc. Math. Extra Vol., Kazuya Kato’s Fiftieth Birthday, 761-788 (2003).

Summary: Let \(m\) be an integer bigger than one, \(A\) a ring of algebraic integers, \(F\) its fraction field, and \(K_m (A)\) the \(m\)-th Quillen \(K\)-group of \(A\). We give a (huge) explicit bound for the order of the torsion subgroup of \(K_m (A)\) (up to small primes), in terms of \(m\), the degree of \(F\) over \(\mathbb Q\), and its absolute discriminant.

MSC:

11R70	\(K\)-theory of global fields
19D99	Higher algebraic \(K\)-theory
19F27	Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects)