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

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)
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