The aim of this paper is to make progress in the understanding of the Scherk– Schwarz dimensional reduction in terms of a compactification in the presence of background fluxes and torsion. From the eleven dimensional supergravity point of view, we find that a general E6(6) S-S phase may be obtained by turning on an appropriate background torsion, together with suitable fluxes, some of which can...

It has long been known that the integral homology of a non-trivial finite group must be non-zero in infinitely many dimensions [15]. Recent work on the Sullivan Conjecture in homotopy theory has made it possible to extend this result to non-acyclic locally finite groups. For more general groups with torsion it becomes more difficult to make such a strong statement. Nevertheless we show that whe...

Stomach torsion is a life-threatening illness of the large dog. There exists only little clarity about the causes. However, dog owners and veterinary surgeons have a good understanding of how the disease progresses after the torsion. Measures during the emergency care of the patients are also well-known, so that in most cases the dogs not only survive a stomach torsion incident, but will not su...

We compute an invariant counting gradient flow lines (including closed orbits) in S-valued Morse theory, and relate it to Reidemeister torsion for manifolds with χ = 0, b1 > 0. Here we extend the results in [6] following a different approach. However, this paper is written in a self-contained manner and may be read independently of [6]. The motivation of this work is twofold: on the one hand, i...

Let R be a discrete valuation ring with algebraically closed residue field, and consider a smooth curve CK over the field of fractions K. For any positive integer r prime to the residual characteristic, we consider the finite K-group scheme PicCK [r] of r-torsion line bundles on CK . We determine when there exists a finite R-group scheme, which is a model of PicCK [r] over R; in other words, we...

We begin with a brief history of the problem of determining the set of points of a curve that map to torsion points of the curve’s Jacobian. Let K be a number field, and suppose that X/K is an algebraic curve of genus g ≥ 2. Assume, furthermore, that X is embedded in its Jacobian variety J via a K-rational Albanese map i; thus there is a K-rational divisor D of degree one on X such that i = iD ...

We introduce a relativized notion of (semi)normalcy for categories that come equipped with a proper stable factorization system, and we use radicals and normal closure operators in order to study torsion theories in such categories. Our results generalize and complement recent studies in the realm of semi-abelian and, in part, homological categories. In particular, we characterize both, torsion...