569 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

### Stabilization of the Witt group

Using an idea due to R.Thomason, we define a "homology theory" on the
category of rings which satisfies excision, exactness, homotopy (in the
algebraic sense) and periodicity of order 4. For regular noetherian rings, we
find P. Balmer's higher Witt groups. For more general rings, this homology
isomorphic to the KT-theory of J. Hornbostel, inspired by the work of B.
Williams. For real or complex C*-algebras, we recover - up to 2 torsion -
topological K-theory.Comment: 6 pages ; see also http://www.math.jussieu.fr/~karoubi

### Hermitian K-theory of the integers

The 2-primary torsion of the higher algebraic K-theory of the integers has
been computed by Rognes and Weibel. In this paper we prove analogous results
for the Hermitian K-theory of the integers with 2 inverted (denoted by Z'). We
also prove in this case the analog of the Lichtenbaum conjecture for the
hermitian K-theory of Z' : the homotopy fixed point set of a suitable Z/2
action on the classifying space of the algebraic K-theory of Z' is the
hermitian K-theory of Z' after 2-adic completion.Comment: 36 pages ; see also http://www.math.jussieu.fr/~karoubi/ and
http://www.math.nus.edu.sg/~matberic

### Generalized differential spaces with $d^N=0$ and the $q$-differential calculus

We present some results concerning the generalized homologies associated with
nilpotent endomorphisms $d$ such that $d^N=0$ for some integer $N\geq 2$. We
then introduce the notion of graded $q$-differential algebra and describe some
examples. In particular we construct the $q$-analog of the simplicial
differential on forms, the $q$-analog of the Hochschild differential and the
$q$-analog of the universal differential envelope of an associative unital
algebra.Comment: 8 pages, Latex2e, uses pb-diagram, available at
http://qcd.th.u-psud.fr, to be published in the Proceedings of the 5th
Colloquium ``Quantum Groups and Integrable Systems", Prague, June 199

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