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We give a new proof of the theorem of Suslin-Voevodsky which shows that the Bloch-Kato conjecture implies a portion of the Beilinson- Lichtenbaum conjectures. Our proof does not rely on resolution of singularities, and thereby extends the Suslin-Voevodsky to positive characteristic.

The Bloch-Kato conjecture and a theorem of Suslin-Voevodsky