Patching the Norm Residue Isomorphism Theorem , by Charles A. Weibel

We provide a patch to complete the proof of the Rost-Voevodsky Theorem, that the norm residue map is an isomorphism. (This settles the motivic Bloch-Kato conjecture). This preprint is designed to be read by experts, to check that the theorem has indeed been proven.

By the norm residue map we mean K_n^M(k)/l → Hⁿ_et(k,μ_lⁿ) for any field k containing 1/l. By "patch" we mean that instead of proving the assertions in [MC/l] about mod-l operations we establish parallel results for operations from integral motivic cohomology to mod-l motivic cohomology.

The unpublished references we depend upon are:

• Rost's Chain Lemma , 1998
• Voevodsky's [MC/l] On Motivic Cohomology with Z/l coefficients, 2003
• Voevodsky's unpublished prepint Operations in motivic cohomology II.
• My preprint [W] Axioms for the Norm Residue Isomorphism, 2006.

• 0844.bib (239 bytes)
• BKpatch.dvi (95260 bytes) [May 23, 2007]
• BKpatch.dvi.gz (38531 bytes)
• BKpatch.pdf (206469 bytes)
• BKpatch.ps.gz (213147 bytes)