207 research outputs found
Model theory and modules
No full textIn recent years the interplay between model theory and other branches of mathematics has led to many deep and intriguing results. In this, the first book on the topic, the theme is the interplay between model theory and the theory of modules. The book is intended to be a self-contained introduction to the subject and introduces the requisite model theory and module theory as it is needed. Dr Prest develops the basic ideas concerning what can be said about modules using the information which may be expressed in a first-order language. Later chapters discuss stability-theoretic aspects of modul
Tensor product of motives via Künneth formula
No full textFollowing Nori's original idea we here provide certain motivic categories with a canonical tensor structure. These motivic categories are associated to a cohomological functor on a suitable base category and the tensor structure is induced by the cartesian tensor structure on the base category via a cohomological Künneth formula
On sheafification of modules
No full textWe consider the localisation of the category of presheaves of modules over a ringed space to the category of sheaves of modules. With a suitable finiteness condition (being "elementary") on the torsion theory, we deduce that over noetherian spaces the latter category is locally finitely presented.
This account is some of the background to our preprint "M. Prest and A. Ralph, Locally finitely presented categories of sheaves of modules" and to that of Philip Bridge, "Local presentability of categories of sheaves of modules"
Definable categories and T-motives
No full textMaking use of Freyd's free abelian category on a preadditive category we show that if T:D→A is a representation of a quiver D in an abelian category A then there is an abelian category A(T), a faithful exact functor FT:A(T)→A and an induced representation T~:D→A(T) such that FTT~=T universally. We then can show that T-motives as well as Nori's motives are given by a certain category of functors on definable categories
Rings of definable scalars of Verma modules
No full textLet M be a Verma module over the Lie algebra, sl2(k), of trace zero 2×2 matrices over
the algebraically closed field k. We show that the ring, R_M, of definable scalars of M
is a von Neumann regular ring and that the canonical map from U(sl2(k)) to R_M is an
epimorphism of rings. We also describe the Ziegler closure of M. The proofs make use
of ideas from the model theory of modules
Freezing orders; the difficulties introduced by the decision in Prest v Petrodel Resources Limited
No full textSimon Ducan, of Moon Beever Solicitors, looks at the way the judgment in Prest v Petrodel Resources Limited [2013] UKSC 34 has received much scrutiny and made reliance on standard form freezing order precedents problematic where the defendant controls various companies that hold the assets that the claimant seeks to freeze. The author suggests that it has served as a reminder that the court will respect and preserve the corporate veil except in very limited circumstances now narrowly defined in the “evasion” principle
Tensor structure for Nori motives
No full textWe construct a tensor product on Freyd’s universal abelian category Ab(C)
attached to an additive tensor category or a tensor-quiver and establish a universal
property. This is used to give an alternative construction for the tensor
product on Nori motives
Model Theory for Sheaves of Modules
No full textWe describe how the model theory of modules is adapted to deal with sheaves of modules
- …
