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1,715
result(s) for
"K-theory."
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Localization for THH(ku) and the topological Hochschild and cyclic homology of Waldhausen categories
The authors develop a theory of THH and TC of Waldhausen categories and prove the analogues of Waldhausen's theorems for K-theory. They resolve the longstanding confusion about localization sequences in THH and TC, and establish a specialized dévissage theorem. As applications, the authors prove conjectures of Hesselholt and Ausoni-Rognes about localization cofiber sequences surrounding THH(ku), and more generally establish a framework for advancing the Rognes program for studying Waldhausen's chromatic filtration on A(*).
eBook
The politics of Harry Potter
\"This political analysis of Harry Potter uses the beloved wizarding world to introduce readers to the equally murky and intimidating world of the political. Readers may be surprised to discover that in fact J.K. Rowling's work provides us with entries into all of the most important political questions in history - from current controversies about terrorism and human rights, to the classic foundations of political thought\"-- Provided by publisher.
BOOK
On the K-theory of pullbacks
To any pullback square of ring spectra we associate a new ring spectrum and use it to describe the failure of excision in algebraic K-theory. The construction of this new ring spectrum is categorical and hence allows us to determine the failure of excision for any localizing invariant in place of K-theory.
As immediate consequences we obtain an improved version of Suslin's excision result in K-theory, generalizations of results of Geisser and Hesselholt on torsion in (bi)relative K-groups, and a generalized version of proexcision for K-theory. Furthermore, we show that any truncating invariant satisfies excision, nilinvariance, and cdh-descent. Examples of truncating invariants include the fibre of the cyclotomic trace, the fibre of the rational Goodwillie–Jones Chern character, periodic cyclic homology in characteristic zero, and homotopy K-theory.
Various of the results we obtain have been known previously, though most of them in weaker forms and with less direct proofs.
Journal Article
Reset : my fight for inclusion and lasting change
The co-founder of the diversity nonprofit Project Include shares the story behind her landmark 2015 lawsuit against powerhouse venture capitalist firm Kleiner Perkins, exploring what her case and refusal to settle revealed about Silicon Valley discrimination.
Book
Witten Non Abelian Localization for Equivariant K-Theory, and the 𝑄,𝑅=0 Theorem
The purpose of the present memoir is two-fold. First, we obtain a non-abelian localization theorem when M is any even dimensional
compact manifold : following an idea of E. Witten, we deform an elliptic symbol associated to a Clifford bundle on M with a vector field
associated to a moment map. Second, we use this general approach to reprove the [Q,R] = 0 theorem of Meinrenken-Sjamaar in the
Hamiltonian case, and we obtain mild generalizations to almost complex manifolds. This non-abelian localization theorem can be used to
obtain a geometric description of the multiplicities of the index of general
eBook
Noncommutative geometry and global analysis : conference in honor of Henri Moscovici, June 29-July 4, 2009, Bonn, Germany
This volume represents the proceedings of the conference on Noncommutative Geometric Methods in Global Analysis, held in honor of Henri Moscovici, from June 29-July 4, 2009, in Bonn, Germany. Henri Moscovici has made a number of major contributions to noncommutative geometry, global analysis, and representation theory. This volume, which includes articles by some of the leading experts in these fields, provides a panoramic view of the interactions of noncommutative geometry with a variety of areas of mathematics. It focuses on geometry, analysis and topology of manifolds and singular spaces, index theory, group representation theory, connections of noncommutative geometry with number theory and arithmetic geometry, Hopf algebras and their cyclic cohomology.
eBook
K-theory of valuation rings
We prove several results showing that the algebraic $K$-theory of valuation rings behaves as though such rings were regular Noetherian, in particular an analogue of the Geisser–Levine theorem. We also give some new proofs of known results concerning cdh descent of algebraic $K$-theory.
Journal Article
Graded K-theory and Leavitt path algebras
Let
G
be a group and
ℓ
a commutative unital
∗
-ring with an element
λ
∈
ℓ
such that
λ
+
λ
∗
=
1
. We introduce variants of hermitian bivariant
K
-theory for
∗
-algebras equipped with a
G
-action or a
G
-grading. For any graph
E
with finitely many vertices and any weight function
ω
:
E
1
→
G
, a distinguished triangle for
L
(
E
)
=
L
ℓ
(
E
)
in the hermitian
G
-graded bivariant
K
-theory category
k
k
G
gr
h
is obtained, describing
L
(
E
) as a cone of a matrix with coefficients in
Z
[
G
]
associated to the incidence matrix of
E
and the weight
ω
. In the particular case of the standard
Z
-grading, and under mild assumptions on
ℓ
, we show that the isomorphism class of
L
(
E
) in
k
k
Z
gr
h
is determined by the graded Bowen–Franks module of
E
. We also obtain results for the graded and hermitian graded
K
-theory of
∗
-algebras in general and Leavitt path algebras in particular which are of independent interest, including hermitian and bivariant versions of Dade’s theorem and of Van den Bergh’s exact sequence relating graded and ungraded
K
-theory.
Journal Article
Corrigendum for the article \Curved Koszul duality theory\
In this corrigendum, we explain and correct a mistake in our article \"Curved Koszul duality theory\". Our definitions of morphisms between semi-augmented properads and between curved coproperads have to be modified.
Dans ce corrigendum, nous expliquons et corrigeons une erreur dans notre article \"Curved Koszul duality theory\". Nos définitions de morphisme entre propérades semi-augmentées et entre coopérades courbées ont été modifiées.
Journal Article