LetX be an n-dimensional algebraic variety over a field of characteristic zero. We describe algebraically defined Deligne 1-motives Alb(X), Alb−(X), Pic(X) and Pic−(X) which generalize the classical Albanese and Picard varieties of a smooth projective variety. We compute Hodge, l-adic and De Rham realizations proving Deligne’s conjecture for H, H2n−1, H 1 and H1. We investigate functoriality, u...

We show that the algebra homomorphism Uq(ĝln) ։ K GLd×C ∗ (Z)⊗C(q) constructed by Ginzburg and Vasserot between the quantum affine algebra of type gln and the equivariant K-theory group of the Steinberg variety (of incomplete flags), specializes to a surjective homomorphism U res ǫ (ĝln) ։ K GLd×C ∗ ǫ (Z). In particular, this shows that the parametrization of irreducible U res ǫ (ŝln)-modules a...

Let G and G be simple Lie groups of equal real rank and real rank at least 2. Let Γ < G and Λ < G be non-uniform lattices. We prove a theorem that often implies that any quasi-isometric embedding of Γ into Λ is at bounded distance from a homomorphism. For example, any quasiisometric embedding of SL(n,Z) into SL(n,Z[i]) is at bounded distance from a homomorphism. We also include a discussion of ...

The paper attempts a systematic study of homomorphisms of relational structures. Such structures are modeled as multialgebras (i.e., relation is represented as a set-valued function). The rst, main, result is that, under reasonable restrictions on the form of the deenition of homomorphism, there are exactly nine compositional homomorphisms of multialgebras. Then the comparison of the obtained c...

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ‎ring of continuous real-valued functions on $L$‎. ‎We show that the‎ ‎lattice $Zid(mathcal{R}L)$ of $z$-ideals of $mathcal{R}L$ is a‎ ‎normal coherent Yosida frame‎, ‎which extends the corresponding $C(X)$‎ ‎result of Mart'{i}nez and Zenk‎. ‎This we do by exhibiting‎ ‎$Zid(mathcal{R}L)$ as a quotient of $Rad(mathcal{R}L)$‎, ‎the‎ ‎...

Cloud computing is one of the widest phenomena embraced in information technology. This result from numerous advantages associated with it making many organizations and individuals offload their data to cloud. Encryption schemes restrict access unauthorized clients, helping attain confidentiality privacy. The modification ciphertext clients’ on cloud demand downloading, deciphering, editing, fi...

in symplectic Floer homology. Both were discovered by Donaldson. They are well defined up to an overall sign. The homomorphism (1) can be interpreted as a relative Donaldson invariant on a 4-manifold with boundary. In other words, this product is obtained by counting anti-self-dual connections over a 4-dimensional cobordism with n+ 1 cylindrical ends corresponding to Yfj . The second homomorphi...