Class and rank of differential modules

A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a substitute for the length of a free complex--and on the rank of a differential module in terms of invariants of its homology. These results specialize to basic theorems in commutative algebra and algebraic topology. One instance is a common generalization of the equicharacteristic case of the New Intersection Theorem of Hochster, Peskine, P. Roberts, and Szpiro, concerning complexes over noetherian commutative rings, and of a theorem of G. Carlsson on differential graded modules over graded polynomial rings.Comment: 27 pages. Minor changes; mainly stylistic. To appear in Inventiones Mathematica

Conversations in a Crowded Room: An Assessment of the Contribution of Historical Research to Criminology

The relationship between history and social science generally, as well as history and criminology specifically, has long been considered problematic. But, since the likes of Burke (1992) and King (1999) spoke of a ‘dialogue of the deaf’, crime history has rapidly expanded and, more latterly, historical criminology has begun to emerge. This article reappraises the relationship of the subject areas by considering the impact that historical research has had on criminology. Although the impact is found to be somewhat patchy, the article identifies positive signs within the two fields that might point towards a more mutually‐enriching future

The effects of weather and temporal variables on calls for police service

SIGLEAvailable from British Library Document Supply Centre- DSC:D061972 / BLDSC - British Library Document Supply CentreGBUnited Kingdo