5 research outputs found
Karoubi's relative Chern character, the rigid syntomic regulator, and the Bloch-Kato exponential map
We construct a variant of Karoubi's relative Chern character for smooth,
separated schemes over the ring of integers in a p-adic field and prove a
comparison with the rigid syntomic regulator. For smooth projective schemes we
further relate the relative Chern character to the etale p-adic regulator via
the Bloch-Kato exponential map. This reproves a result of Huber and Kings for
the spectrum of the ring of integers and generalizes it to all smooth
projective schemes as above.Comment: v1:33 pages; v2:major revision (28 pages); v3:minor changes; v4:minor
changes following suggestions by a refere
Hermitian K-theory and 2-regularity for totally real number fields
We completely determine the 2-primary torsion subgroups of the hermitian
K-groups of rings of 2-integers in totally real 2-regular number fields. The
result is almost periodic with period 8. We also identify the homotopy fibers
of the forgetful and hyperbolic maps relating hermitian and algebraic K-theory.
The result is then exactly periodic of period 8. In both the orthogonal and
symplectic cases, we prove the 2-primary hermitian Quillen-Lichtenbaum
conjecture.Comment: To appear in Mathematische Annale
FROM ACYCLIC GROUPS TO THE BASS CONJECTURE FOR AMENABLE GROUPS
International audienceWe prove that the Bost Conjecture on the -assembly map for countable discrete groups implies the Bass Conjecture. It follows that all amenable groups satisfy the Bass Conjecture
Homotopy idempotents on manifolds and Bass' conjectures
This is the version published by Geometry & Topology Monographs on 29 January 2007International audienceThe Bass trace conjectures are placed in the setting of homotopy idempotent selfmaps of manifolds. For the strong conjecture, this is achieved via a formulation of Geoghegan. The weaker form of the conjecture is reformulated as a comparison of ordinary and L^2-Lefschetz numbers
Finite index subgroups of mapping class groups
Let and , and let be the mapping class group of a surface of genus with boundary components. We prove that contains a unique subgroup of index up to conjugation, a unique subgroup of index up to conjugation, and the other proper subgroups of are of index greater than . In particular, the minimum index for a proper subgroup of is