let φ be a w  -continuous homomorphism from a dual banach algebra to c. the notion of φ-connes amenability is studied and some characterizations is given. a type of diagonal for dual banach algebras is dened. it is proved that the existence of such a diagonal is equivalent to φ-connes amenability. it is also shown that φ-connes amenability is equivalent to so-called φ-splitting of a certain s...

Let X and S denote algebraic stacks of finite type over the field C of complex numbers, and let X and S denote their analytifications (which are stacks in the complex analytic setting). Analytification gives a functor φ : HomC(S,X) → Hom(S , X). It is natural to ask for circumstances under which φ is an equivalence. In the case where X and S are projective schemes, a satisfactory answer was obt...

We introduce a new concept in the area of formal logic: axioms for model morphisms. We work in the setting of specification languages that define the semantics of a theory as a category of models. While it is routine to use axioms to specify the class of models of a theory, there has so far been no analogue to systematically specify the morphisms between these models. This leads to subtle probl...

Let K be a function field in one variable over an arbitrary field F. Given a rational function φ ∈ K(z) of degree at least two, the associated canonical height on the projective line was defined by Call and Silverman. The preperiodic points of φ all have canonical height zero; conversely, if F is a finite field, then every point of canonical height zero is preperiodic. However, if F is an infin...

We define the notion of K-covering of automata with multiplicity (in a semiring K) that extend the one of covering of automata. We make use of this notion, together with the Schützenberger construct that we have explained in a previous work and that we briefly recall here, in order to give a direct and constructive proof of a fundamental theorem on N-rational power series. In a previous work (c...

Let A be a fixed ring, and consider the projective space PA = ProjA[x0, . . . , xn] over A. On PA we have the invertible sheaf O(1), and the homogenous coordinates x0, . . . , xn give rise to global sections ẋ0, . . . , ẋn ∈ Γ(PA,O(1)). Throughout this section we drop the dot in this notation and just write xi for the global section of O(1). One sees easily that the sheaf O(1) is generated by t...

Let R be a ring and consider the category ModR of (right) R-modules. Given a class C ofR-modules, a morphismM → N in ModR is called a left C-approximation of M provided that N belongs to C and the induced morphism HomR(N,C) → HomR(M,C) is surjective for every C in C. This concept has been introduced by Auslander and Smalø [2], and independently by Enochs [5]. Approximations arise naturally in v...

Let X be an irreducible smooth complex projective curve of genus g > 2, and let x ∈ X be a fixed point. A framed bundle is a pair (E,φ), where E is a vector bundle over X, of rank r and degree d, and φ : Ex −→ C r is a non–zero homomorphism. There is a notion of (semi)stability for framed bundles depending on a parameter τ > 0, which gives rise to the moduli space of τ– semistable framed bundle...