14,844 research outputs found
A Passive Balance-of-Payments Strategy for the United States
macroeconomics, balance-of-payments
The Bousfield lattice of a triangulated category and stratification
For a tensor triangulated category which is well generated in the sense of
Neeman, it is shown that the collection of Bousfield classes forms a set. This
set has a natural structure of a complete lattice which is then studied, using
the notions of stratification and support.Comment: 25 pages; minor changes from earlier version; this will appear in the
Math.
Potentiality and Contradiction in Quantum Mechanics
Following J.-Y.B\'eziau in his pioneer work on non-standard interpretations
of the traditional square of opposition, we have applied the abstract structure
of the square to study the relation of opposition between states in
superposition in orthodox quantum mechanics in \cite{are14}. Our conclusion was
that such states are \ita{contraries} (\ita{i.e.} both can be false, but both
cannot be true), contradicting previous analyzes that have led to different
results, such as those claiming that those states represent \ita{contradictory}
properties (\ita{i. e.} they must have opposite truth values). In this chapter
we bring the issue once again into the center of the stage, but now discussing
the metaphysical presuppositions which underlie each kind of analysis and which
lead to each kind of result, discussing in particular the idea that
superpositions represent potential contradictions. We shall argue that the
analysis according to which states in superposition are contrary rather than
contradictory is still more plausible
Localising subcategories for cochains on the classifying space of a finite group
The localising subcategories of the derived category of the cochains on the
classifying space of a finite group are classified. They are in one to one
correspondence with the subsets of the set of homogeneous prime ideals of the
cohomology ring .Comment: 5 pages, minor changes, accepted for publication in C. R. Math. Acad.
Sci. Pari
Local cohomology and support for triangulated categories
We propose a new method for defining a notion of support for objects in any
compactly generated triangulated category admitting small coproducts. This
approach is based on a construction of local cohomology functors on
triangulated categories, with respect to a central ring of operators. Suitably
specialized one recovers, for example, the theory for commutative noetherian
rings due to Foxby and Neeman, the theory of Avramov and Buchweitz for complete
intersection local rings, and varieties for representations of finite groups
according to Benson, Carlson, and Rickard. We give explicit examples of objects
whose triangulated support and cohomological support differ. In the case of
group representations, this allows us to correct and establish a conjecture of
Benson.Comment: 40 pages. Relatively minor changes (clarifications, corrections, new
references, etc). This article will appear in the Ann. Sci. Ecole Norm. Su
Stratifying modular representations of finite groups
We classify localising subcategories of the stable module category of a
finite group that are closed under tensor product with simple (or, equivalently
all) modules. One application is a proof of the telescope conjecture in this
context. Others include new proofs of the tensor product theorem and of the
classification of thick subcategories of the finitely generated modules which
avoid the use of cyclic shifted subgroups. Along the way we establish similar
classifications for differential graded modules over graded polynomial rings,
and over graded exterior algebras.Comment: 37 pages; minor changes from the first version. This is slated to
appear in the January 2012 issue of Annals of Math., volume 175, no.
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