The category of admissible (in the appropriately modified sense of representation theory of totally disconnected groups) semi-linear representations of the automorphism group of an algebraically closed extension of infinite transcendence degree of the field of algebraic complex numbers is described. Let k be a field of characteristic zero containing all ℓ-primary roots of unity for a prime ℓ, F...

The category of admissible (in the appropriately modified sense of representation theory of totally disconnected groups) semi-linear representations of the automorphism group of an algebraically closed extension of infinite transcendence degree of the field of algebraic complex numbers is described. Let k be a field of characteristic zero containing all ℓ-primary roots of unity for a prime ℓ, F...

should hold for X smooth proper, where CH(X)Q is the Chow group of X with rational coefficients, and QX denotes the constant object in D MM(X), the bounded derived category of MM(X). In this paper we give a formalism of mixed sheaves which might be useful for the construction of mixed motivic sheaves. Let k be a field embeddable in C, and V(k) the category of separated algebraic varieties over ...

We use some detailed knowledge of the cohomology ring real Grassmann manifolds G k (ℝ n ) to compute zero-divisor cup-length and estimate topological complexity motion planning for -linear subspaces in ℝ . In addition, we obtain results about monotonicity Lusternik–Schnirelmann category as a function

If A is a bialgebra over a field k, a left-right Yetter-Drinfel’d module over A is a k-linear space M which is a left A-module, a right A-comodule and such that a certain compatibility condition between these two structures holds. YetterDrinfel’d modules were introduced by D. Yetter in [18] under the name of “crossed bimodules” (they are called “quantum Yang-Baxter modules” in [5]; the present ...

n this paper we study the Hyers-Ulam-Rassias stability of Cauchyequation in Felbin's type fuzzy normed linear spaces. As a resultwe give an example of a fuzzy normed linear space such that thefuzzy version of the stability problem remains true, while it failsto be correct in classical analysis. This shows how the category offuzzy normed linear spaces differs from the classical normed linearspac...

We define Homotopy quantum field theories (HQFT) as Topological quantum field theories (TQFT) for manifolds endowed with extra structure in the form of a map into some background space X. We also build the category of homotopy cobordisms HCobord(n, X) such that an HQFT is a functor from this category into a category of linear spaces. We then derive some very general properties of HCobord(n, X),...

Definition 1.1. A weak factorization system (L,R) in a category K consists of two classes L and R of morphisms of K such that (1) R = L , L = R and (2) any morphism h of K has a factorization h = gf with f ∈ L and g ∈ R. Definition 1.2. A model category is a complete and cocomplete category K together with three classes of morphisms F , C and W called fibrations, cofibrations and weak equivalen...

Let G = GL(N), K = GL(p)× GL(q), where p + q = N , and let n be a positive integer. We construct a functor from the category of HarishChandra modules for the pair (G,K) to the category of representations of the degenerate affine Hecke algebra of type Bn, and a functor from the category of K-monodromic twisted D-modules on G/K to the category of representations of the degenerate double affine He...

We propose a notion of weak (n + k, n)-category, which we call (n + k, n)Θ-spaces. The (n + k, n)-Θ-spaces are precisely the fibrant objects of a certain model category structure on the category of presheaves of simplicial sets on Joyal’s category Θn. This notion is a generalization of that of complete Segal spaces (which are precisely the (∞, 1)-Θ-spaces). Our main result is that the above mod...