Let X be a non-singular projective threefold over an algebraically closed field of any characteristic, and let A(X) be the group of algebraically trivial codimension 2 algebraic cycles on X modulo rational equivalence with coefficients in Q. Assume X is birationally equivalent to another threefold X ′ admitting a fibration over an integral curve C whose generic fiber X ′ η̄, where η̄ = Spec(k(C))...

Homomorphisms h:F ! * G are studied, where F is a free group and * G is the free product. In Part I, the conditions imposed on the homomorphism h relate to certain commutators in F . The method of proof is to obtain a topological realization of h, interpreting F as the fundamental group of a surface with boundary and * G as the fundamental group of a wedge of complexes. Standard general positio...

Let Emb(Sj, Sn) denote the space of C∞–smooth embeddings of the j–sphere in the n–sphere. This paper considers homotopy-theoretic properties of the family of spaces Emb(Sj, Sn) for n ≥ j > 0. There is a homotopy-equivalence Emb(Sj, Sn) ' SOn+1 ×SOn−j Kn,j where Kn,j is the space of embeddings of Rj in Rn which are standard outside of a ball. The main results of this paper are that Kn,j is (2n−3...

Abstract. We combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if A1 and A2 are operator algebras, then any bounded epimorphism of A1 onto A2 is completely bounded provided that A2 contains a norming C ∗-subalgebra. We use this result to give some insights into Kadison’s Similarity Problem: we show that every faithful bounded homomo...

1.1. Algebra case. Let A be a filtered quantization of a Z-graded finitely generated Poisson algebra A. By A -mod we denote the category of finitely generated A-modules. A basic tool to study such modules is to reduce them to finitely generated A-modules that can be studied by means of Commutative algebra/ Algebraic geometry. Given an A-module M , one introduces the notion of a good filtration ...

For any module M over an associative ring R, let σ[M ] denote the smallest Grothendieck subcatgory of Mod-R containingM . If σ[M ] is locally finitely presented the notions of purity and pure injectivity are defined in σ[M ]. In this paper the relationship between these notions and the corresponding notions defined in Mod-R are investigated, and the connection between the resulting Ziegler spec...

We propose a new approach to superrigidity phenomena and implement it for lattice representations and measurable cocycles with Homeo+(S ) as the target group. We are motivated by Ghys’ theorem stating that any representation ̺ : Γ → Homeo+(S ) of an irreducible lattice Γ in a semi-simple real Lie group G of higher rank, either has a finite orbit or, up to a semi-conjugacy, extends to G which act...

It is a well-known fact that every group G has a presentation of the form G = F/R, where F is a free group and R the kernel of the natural epimorphism from F onto G. Driven by the desire to obtain a similar presentation of the group of automorphisms Aut(G), we can consider the subgroup Stab(R) ⊆ Aut(F ) of those automorphisms of F that stabilize R, and try to figure out if the natural homomorph...

In this paper, we have established an intimate connection between near-nings and linear automata, and obtain the following results: 1) For a near-ring N there exists a linear GSA S with   N N  S iff (a) is abelian, (b) N has an identity 1, (c) There is some such that is generated by {1,d}; 2) Let  , N  : h   d d N  0 N  S S be a GSAepimorphism. Then there exists a near-ring epimorphism...

The aim of this paper is to describe Quillen model category structures on the category CatC of internal categories and functors in a given finitely complete category C. Several non-equivalent notions of internal equivalence exist; to capture these notions, the model structures are defined relative to a given Grothendieck topology on C. Under mild conditions on C, the regular epimorphism topolog...