Let R be a commutative ring whose complete ring of quotients is Rinjective. We show that the category of topological R-modules contains a full subcategory that is ∗-autonomous using R itself as dualizing object. In order to do this, we develop a new variation on the category chu(D, R), where D is the category of discrete R-modules: the high wide subcategory, which we show equivalent to the cate...

Let CRF S denote the category of S-colored rooted forests, and HCRFS denote its Ringel-Hall algebra as introduced in [6]. We construct a homomorphism from a K+ 0 (CRF S)–graded version of the Hopf algebra of noncommutative symmetric functions to HCRFS . Dualizing, we obtain a homomorphism from the Connes-Kreimer Hopf algebra to a K+ 0 (CRF S)–graded version of the algebra of quasisymmetric func...

A general eventual freeness result is given for nef and big line bundles in positive characteristic. One application is to the geometry of the universal stable curve over Mg , specifically, the eventual freeness of the relative dualizing sheaf, in positive characteristic. An example is given which shows this fails in characteristic zero. A second application is to Mori’s program for minimal mod...

is finite under the following equivalence (cf. Theorem 3.1). For stable curves X and Y over OK , X is equivalent to Y if X ⊗OK OK′ ≃ Y ⊗OK OK′ for some finite extension field K ′ of K. In §1, we will consider semistability of the kernel of H(C,L) ⊗ OC → L, which gives a generalization of [PR]. In §2, an inequality of self-intersection and height will be treated. Finally, §3 is devoted to finite...

Upper and lower envelope representations are developed for value functions associated with problems of optimal control and the calculus of variations that are fully convex, in the sense of exhibiting convexity in both the state and the velocity. Such convexity is used in dualizing the upper envelope representations to get the lower ones, which have advantages not previously perceived in such ge...

We study hyperkähler cones and their corresponding quaternion-Kähler spaces. We present a classification of 4(n − 1)-dimensional quaternionKähler spaces with n abelian quaternionic isometries, based on dualizing superconformal tensor multiplets. These manifolds characterize the geometry of the hypermultiplet sector of perturbative moduli spaces of type-II strings compactified on a Calabi-Yau ma...

Introduction 1 0.1. Associated primes 2 0.2. Depth 2 1. Regular local rings and their cohomological properties 4 1.1. Notions of dimension 4 1.2. Dualizing functor 5 1.3. Local rings 6 1.4. Serre’s theorem on regular local rings 6 1.5. Cohomology of D when global dimension is finite 8 2. Depth 8 2.1. Property (Sk) 8 2.2. Serre’s criterion of normality 10 2.3. Cohen-Macaulay modules 11 3. Diviso...

A flippable edge in an acyclic digraph is an edge whose reorientation leaves the graph acyclic. We characterize the spanning trees T of an undirected graph G such that there exists an acyclic orientation of G whose set of flippable edges is T . In particular for every edge e ∈ E(G) we give a linear algorithm returning an acyclic orientation and a spanning tree T containing e such that T is the ...