928 research outputs found
A new proof for the decidability of D0L ultimate periodicity
We give a new proof for the decidability of the D0L ultimate periodicity
problem based on the decidability of p-periodicity of morphic words adapted to
the approach of Harju and Linna.Comment: In Proceedings WORDS 2011, arXiv:1108.341
Spectra of units for periodic ring spectra and group completion of graded E-infinity spaces
We construct a new spectrum of units for a commutative symmetric ring
spectrum that detects the difference between a periodic ring spectrum and its
connective cover. It is augmented over the sphere spectrum. The homotopy
cofiber of its augmentation map is a non-connected delooping of the usual
spectrum of units whose bottom homotopy group detects periodicity.
Our approach builds on the graded variant of E-infinity spaces introduced in
joint work with Christian Schlichtkrull. We construct a group completion model
structure for graded E-infinity spaces and use it to exhibit our spectrum of
units functor as right adjoint on the level of homotopy categories. The
resulting group completion functor is an essential tool for studying ring
spectra with graded logarithmic structures.Comment: v3: 33 pages; exposition improved, accepted for publication in
Algebraic and Geometric Topolog
kk-Theory for Banach Algebras I: The Non-Equivariant Case
kk is a bivariant K-theory for Banach algebras that has
reasonable homological properties, a product and is Morita invariant in a very
general sense. We define it here by a universal property and ensure its
existence in a rather abstract manner using triangulated categories. The
definition ensures that there is a natural transformation from Lafforgue's
theory KK into it so that one can take products of elements in
KK that lie in kk.Comment: 43 page
Noncommutative Kn\"{o}rrer periodicity and noncommutative Kleinian singularities
We establish a version of Kn\"{o}rrer's Periodicity Theorem in the context of
noncommutative invariant theory. Namely, let be a left noetherian
AS-regular algebra, let be a normal and regular element of of positive
degree, and take . Then there exists a bijection between the set of
isomorphism classes of indecomposable non-free maximal Cohen-Macaulay modules
over and those over (a noncommutative analog of) its second double branched
cover . Our results use and extend the study of twisted matrix
factorizations, which was introduced by the first three authors with Cassidy.
These results are applied to the noncommutative Kleinian singularities studied
by the second and fourth authors with Chan and Zhang.Comment: Numerous typos fixed, removed unnecessary finite order hypothesi
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