Let X be a smooth projective scheme of dimension d ≥ 1 over the field k, and let C be an indecomposable coherent sheaf on X . Then there is an Auslander-Reiten sequence in the category of quasi-coherent sheaves on X , 0 → (ΣC)⊗ ω −→ B −→ C → 0. Here ΣC is the (d−1)’st syzygy in a minimal injective resolution of C, and ω is the dualizing sheaf of X . 0. Introduction This note shows that Auslande...

Let p be an odd prime number and let S be a finite set of prime numbers congruent to 1 modulo p. We prove that the group GS(Q)(p) has cohomological dimension 2 if the linking diagram attached to S and p satisfies a certain technical condition, and we show that GS(Q)(p) is a duality group in these cases. Furthermore, we investigate the decomposition behaviour of primes in the extension QS(p)/Q a...

We study general structured corecursion, dualizing the work of Osius, Taylor, and others on general structured recursion. We call an algebra of a functor corecursive if it supports general structured corecursion: there is a unique map to it from any coalgebra of the same functor. The concept of antifounded algebra is a statement of the bisimulation principle. We show that it is independent from...

The large N limit of D3-branes is expected to correspond to a superconformal field theory living on the boundary of the anti-de Sitter space appearing in the near-horizon geometry. Dualizing the D3-brane to a D-instanton, we show that this limit is equivalent to a type IIB S-duality. In both cases one effectively reaches the near-horizon geometry. This provides an alternative approach to an ear...

Axioms ruling linear negation have been investigated in the context of the complete semantics for distributive intuitionistic linear logic. Among these are the condition of being a dualizing element and the one of being a cyclic element. The motivation for analyzing other syntactic constraints comes from the observation that groupoids are models for classical linear logic. The analysis proceeds...

Motivated by issues in designing practical total functional programming languages, we are interested in structured recursive equations that uniquely describe a function not because of the properties of the coalgebra marshalling the recursive call arguments but thanks to the algebra assembling their results. Dualizing the known notions of recursive and wellfounded coalgebras, we call an algebra ...

Let K be a d-dimensional convex body, and let K be the intersection of n halfspaces containing K whose bounding hyperplanes are independent and identically distributed. Under suitable distributional assumptions, we prove an asymptotic formula for the expectation of the difference of the mean widths of K and K, and another asymptotic formula for the expectation of the number of facets of K. Thes...

Dialectica categories are a very versatile categorical model of linear logic. They have been used to model many seemingly different systems, for example Petri nets and the Lambek calculus. In this note, we expand our previous work on fuzzy Petri nets to deal with fuzzy topological systems. One basic idea is to use as the dualizing object in the Dialectica categories construction, the unit real ...

1. The construction of T(A) is motivated by dualizing the fundamental group 7Ti(X) of a differentiable manifold X with a base point Xo. Let A be the -R-algebra of C functions on X equipped with the derivation d, which is the usual differentiation from A into the Amodule M = ÛA of C 1-forms on X. Recall that the shuffle algebra Sh(M) consists of the i£-module of the tensor algebra TR(M) and the ...

We argue that apart from the standard closed and open strings one may consider a third possibility that we call monodromic strings. The monodromic string propagating on a target looks like an ordinary open string (a mapping from a segment to the target) but its space of states is isomorphic to that of a closed string. It is shown that the monodromic strings naturally appear in T-dualizing close...