By the Telescope Conjecture for Module Categories, we mean the following claim: “Let R be any ring and (A,B) be a hereditary cotorsion pair in Mod-R with A and B closed under direct limits. Then (A,B) is of finite type.” We prove a modification of this conjecture with the word ‘finite’ replaced by ‘countable’. We show that a hereditary cotorsion pair (A,B) of modules over an arbitrary ring R is...

Reened quantum invariants for closed three-manifolds with links and spin structures are extended to a Topological Quantum Field Theory. By a `universal con-struction', one associates, to surfaces with structure, modules which are shown to be free of nite rank. These modules satisfy the multiplicativity axiom of TQFT in an extended Z=2-graded sense, and their ranks are given by a spin reened ver...

Let G be a finite group and let T (G) be the abelian group of equivalence classes of endotrivial kG-modules, where k is an algebraically closed field of characteristic p. We determine, in terms of the structure of G, the kernel of the restriction map from T (G) to T (S), where S is a Sylow p-subgroup of G, in the case when S is abelian. This provides a classification of all torsion endotrivial ...

1. Introduction. Let © be a Lie algebra over a field A. A decomposition of © is a triple (ni, b, n2) of subalgebras of © such that ® = niffif)©n2 a vector space direct sum and such that [b, n,-]Cn< for 4 = 1, 2. In [5] we showed how one could "induce" ©-modules from b-modules in a natural manner. In this paper we prove a useable necessary and sufficient condition that a ©-module must satisfy in...

Let R be a commutative Noetherian local ring with residue field k. X resolving subcategory of finitely generated R-modules. This paper mainly studies when contains k or consists totally reflexive modules. It is proved that does so if closed under cosyzygies. A conjecture Dao and Takahashi also shown to hold in several cases.

In this paper we prove a topological lemma on real valued random variables which implies the basic ingredients for the proof of the Fundamental Theorem of Asset Pricing in the two period case. In particular, previous results of Stricker, 9], and of Schachermayer, 6], are special cases of our result. Our proof is considerably shorter and more transparent than previous proofs of related special c...

We investigate the abelian category which is the target of intersection homology. Recall that, given a stratified space X, we get intersection homology groups IHnX depending on the choice of an n-perversity p. The n-perversities form a lattice, and we can think of IHnX as a functor from this lattice to abelian groups, or more generally R-modules. Such perverse R-modules form a closed symmetric ...

We follow throughout a heterogeneous approach to present some characterizations (Theorem 3.5 and Theorem 3.35) of subdirectly irreducible bijective Boolean modules. The notions of essential element (as modular element) and [1]-closed element (as Boolean element) were implemented to this class of algebras. Our final aim of reaching the class of simple bijective Boolean modules, as a particular c...

We study bundles on rank 4 maximal orders on P ramified on a smooth plane quartic. We compute the possible Chern classes for line bundles. Our main result is that the moduli space of line bundles with minimal second Chern class is either a point or a smooth genus two curve. Throughout, all objects and maps are assumed to be defined over some algebraically closed base field k of characteristic 0...

We study conditions for a concurrent construction of proof-nets in the framework developed by Andreoli in recent papers. We define specific correctness criteria for that purpose. We first study closed modules (i.e. validity of the execution of a logic program), then extend the criterion to open modules (i.e. validity during the execution) distinguishing criteria for acyclicity and connectabilit...