34 research outputs found
Infinitesimal cohomology and the Chern character to negative cyclic homology
There is a Chern character from K-theory to negative cyclic homology. We show
that it preserves the decomposition coming from Adams operations, at least in
characteristic 0. This is done by using infinitesimal cohomology to reduce to
the case of a nilpotent ideal (which had been established by Cathelineau some
time ago).Comment: Included reference for identification of relative Chern and rational
homotopy theory characters; some minor editing for clarit
A negative answer to a question of Bass
In this companion paper to arXiv:0802.1928 we provide an example of an
isolated surface singularity over a number field such that but . This answers, negatively, a
question of Bass.Comment: The paper was previously part of arXiv:0802.192
Bass’ \u3ci\u3eNK\u3c/i\u3e groups and \u3ci\u3ecd h\u3c/i\u3e-fibrant Hochschild homology
The K-theory of a polynomial ring R[t ] contains the K-theory of R as a summand. For R commutative and containing Q, we describe K∗(R[t ])/K∗(R) in terms of Hochschild homology and the cohomology of Kähler differentials for the cdh topology.
We use this to address Bass’ question, whether Kn(R) = Kn(R[t ]) implies Kn(R) = Kn(R[t1, t2]). The answer to this question is affirmative when R is essentially of finite type over the complex numbers, but negative in general
Bass' groups and -fibrant Hochschild homology
The -theory of a polynomial ring contains the -theory of as
a summand. For commutative and containing \Q, we describe
in terms of Hochschild homology and the cohomology of
K\"ahler differentials for the topology. We use this to address Bass'
question, on whether implies . The
answer is positive over fields of infinite transcendence degree; the companion
paper arXiv:1004.3829 provides a counterexample over a number field.Comment: The article was split into two parts on referee's suggestion in
4/2010. This is the first part; the second can be found at arXiv:1004.382
On the vanishing of negative K-groups
Let k be an infinite perfect field of positive characteristic p and assume
that strong resolution of singularities holds over k. We prove that, if X is a
d-dimensional noetherian scheme whose underlying reduced scheme is essentially
of finite type over the field k, then the negative K-group K_q(X) vanishes for
every q < -d. This partially affirms a conjecture of Weibel.Comment: Math. Ann. (to appear
Cohomological Hasse principle and motivic cohomology for arithmetic schemes
In 1985 Kazuya Kato formulated a fascinating framework of conjectures which
generalizes the Hasse principle for the Brauer group of a global field to the
so-called cohomological Hasse principle for an arithmetic scheme. In this paper
we prove the prime-to-characteristic part of the cohomological Hasse principle.
We also explain its implications on finiteness of motivic cohomology and
special values of zeta functions.Comment: 47 pages, final versio
K-regularity, cdh-fibrant hochschild homology, and a conjecture of vorst
Fil:Cortiñas, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina
Bass’ \u3ci\u3eNK\u3c/i\u3e groups and \u3ci\u3ecd h\u3c/i\u3e-fibrant Hochschild homology
The K-theory of a polynomial ring R[t ] contains the K-theory of R as a summand. For R commutative and containing Q, we describe K∗(R[t ])/K∗(R) in terms of Hochschild homology and the cohomology of Kähler differentials for the cdh topology.
We use this to address Bass’ question, whether Kn(R) = Kn(R[t ]) implies Kn(R) = Kn(R[t1, t2]). The answer to this question is affirmative when R is essentially of finite type over the complex numbers, but negative in general