Asymptotic Behavior of Ext functors for modules of finite complete intersection dimension

Let $R$ be a local ring, and let $M$ and $N$ be finitely generated $R$-modules such that $M$ has finite complete intersection dimension. In this paper we define and study, under certain conditions, a pairing using the modules \Ext_R^i(M,N) which generalizes Buchweitz's notion of the Herbrand diference. We exploit this pairing to examine the number of consecutive vanishing of \Ext_R^i(M,N) needed to ensure that \Ext_R^i(M,N)=0 for all $i\gg 0$. Our results recover and improve on most of the known bounds in the literature, especially when $R$ has dimension at most two

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Peer reviewe

Tourism and toponymy: Commodifying and Consuming Place Names

Academic geographers have a long history of studying both tourism and place names, but have rarely made linkages between the two. Within critical toponymic studies there is increasing debate about the commodification of place names, but to date the role of tourism in this process has been almost completely overlooked. In some circumstances, toponyms can become tourist sights based on their extraordinary properties, their broader associations within popular culture, or their role as metanyms for some other aspect of a place. Place names may be sights in their own right or ‘markers’ of a sight and, in some cases, the marker may be more significant than the sight to which it refers. The appropriation of place names through tourism also includes the production and consumption of a broad range of souvenirs based on reproductions or replicas of the material signage that denote place names. Place names as attractions are also associated with a range of performances by tourists, and in some cases visiting a place name can be a significant expression of fandom. In some circumstances, place names can be embraced and promoted by tourism marketing strategies and are, in turn, drawn into broader circuits of the production and consumption of tourist space