497 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
On the cohomological spectrum and support varieties for infinitesimal unipotent supergroup schemes
We show that if is an infinitesimal elementary supergroup scheme of
height , then the cohomological spectrum of is naturally
homeomorphic to the variety of supergroup homomorphisms
from a certain (non-algebraic) affine
supergroup scheme into . In the case , we further
identify the cohomological support variety of a finite-dimensional
-supermodule as a subset of . We then discuss how our
methods, when combined with recently-announced results by Benson, Iyengar,
Krause, and Pevtsova, can be applied to extend the homeomorphism
to arbitrary infinitesimal unipotent supergroup
schemes.Comment: Fixed some algebra misidentifications, primarily in Sections 1.3 and
3.3. Simplified the proof of Proposition 3.3.
Higher homotopy of groups definable in o-minimal structures
It is known that a definably compact group G is an extension of a compact Lie
group L by a divisible torsion-free normal subgroup. We show that the o-minimal
higher homotopy groups of G are isomorphic to the corresponding higher homotopy
groups of L. As a consequence, we obtain that all abelian definably compact
groups of a given dimension are definably homotopy equivalent, and that their
universal cover are contractible.Comment: 13 pages, to be published in the Israel Journal of Mathematic
On Fields of rationality for automorphic representations
This paper proves two results on the field of rationality \Q(\pi) for an
automorphic representation , which is the subfield of \C fixed under the
subgroup of \Aut(\C) stabilizing the isomorphism class of the finite part of
. For general linear groups and classical groups, our first main result is
the finiteness of the set of discrete automorphic representations such
that is unramified away from a fixed finite set of places,
has a fixed infinitesimal character, and [\Q(\pi):\Q] is bounded. The second
main result is that for classical groups, [\Q(\pi):\Q] grows to infinity in a
family of automorphic representations in level aspect whose infinite components
are discrete series in a fixed -packet under mild conditions
Maximal equicontinuous factors and cohomology for tiling spaces
We study the homomorphism induced on cohomology by the maximal equicontinuous
factor map of a tiling space. We will see that this map is injective in degree
one and has torsion free cokernel. We show by example, however, that the
cohomology of the maximal equicontinuous factor may not be a direct summand of
the tiling cohomology
McShane-type Identities for Affine Deformations
We derive an identity for Margulis invariants of affine deformations of a
complete orientable one-ended hyperbolic sur- face following the identities of
McShane, Mirzakhani and Tan- Wong-Zhang. As a corollary, a deformation of the
surface which infinitesimally lengthens all interior simple closed curves must
in- finitesimally lengthen the boundary.Comment: resubmitted after error revising another submissio
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