Periodicity of hermitian K-groups

Details Periodicity of hermitian K-groups Periodicity of hermitian K-groups

2011-01-11

arxiv.org/abs/1101.2056v1

Mathematics

K-Theory and Homology

Scientific paper

Bott periodicity for the unitary, orthogonal and symplectic groups is fundamental to topological K-theory. Analogous to unitary topological K-theory, for algebraic K-groups with finite coefficients similar periodicity results are consequences of the Milnor and Bloch-Kato conjectures, affirmed by Voevodsky, Rost and others. More generally, we prove that periodicity of the algebraic K-groups for any ring implies periodicity for its hermitian K-groups, analogous to orthogonal and symplectic topological K-theory. The proofs use in an essential way higher KSC theories extending those of Anderson and Green. They also provide an upper bound for the higher hermitian K-groups in terms of the higher algebraic K-groups. We also relate periodicity to etale hermitian K-groups by proving ahermitian version of Thomason's etale descent theorem. The results are illustrated in detail for local fields, rings of integers in number fields, smooth complex algebraic varieties, rings of continuous functions on compact spaces, and group rings.

Affiliated with

Also associated with

No associations

Rating

Periodicity of hermitian K-groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Periodicity of hermitian K-groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Periodicity of hermitian K-groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-159991