#### DOCUMENTA MATHEMATICA, Extra Volume: Kazuya Kato's Fiftieth Birthday (2003), 761-788

Christophe Soulé

A Bound for the Torsion in the $K$-Theory of Algebraic Integers

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 $\mathbf Q$, and its absolute discriminant.

2000 Mathematics Subject Classification:

Keywords and Phrases:

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