The paper examines the current transformation and spatial restructuring of the urban economy with focus on the location dynamics of business services, especially during the past decade of economic ...growth. Since the early 1990s, Copenhagen has experienced economic growth and job creation created mainly by the service industries, including the rise of knowledge intensive business services. The location dynamics of the 1990s growth were more ambiguous than the patterns of the 1980s. The location in the 1990s involved both a concentration in the central part of the urban landscape, an extension of existing locations in suburbia and growth in new locations in the urban landscape. The paper provides empirical evidence of the new complexity of location dynamics and introduces imaginary spaces of location to explain the diversity of location. Imaginary spaces of location are social construction of firms based on the perception, experience and interpretation of the firm’s location.
Linkage classes of grade 3 perfect ideals Christensen, Lars Winther; Veliche, Oana; Weyman, Jerzy
Journal of pure and applied algebra,
June 2020, 2020-06-00, Letnik:
224, Številka:
6
Journal Article
Recenzirano
Odprti dostop
While every grade 2 perfect ideal in a regular local ring is linked to a complete intersection ideal, it is known not to be the case for ideals of grade 3. We soften the blow by proving that every ...grade 3 perfect ideal in a regular local ring is linked to a complete intersection or a Golod ideal. Our proof is indebted to a homological classification of Cohen–Macaulay local rings of codimension 3. That debt is swiftly repaid, as we use linkage to reveal some of the finer structures of this classification.
Let p be a prime ideal in a commutative noetherian ring R and denote by k(p) the residue field of the local ring R_p. We prove that if an R-module M satisfies Ext_R^n(k(p),M) = 0 for some n >= dim R, ...then Ext_R^i(k(p),M) = 0 holds for all i >= n. This improves a result of Christensen, Iyengar, and Marley by lowering the bound on n. We also improve existing results on Tor-rigidity. This progress is driven by the existence of minimal semi-flat-cotorsion replacements in the derived category as recently proved by Nakamura and Thompson.
Gorenstein homological dimensions are refinements of the classical homological dimensions, and finiteness singles out modules with amenable properties reflecting those of modules over Gorenstein ...rings.
As opposed to their classical counterparts, these dimensions do not immediately come with practical and robust criteria for finiteness, not even over commutative noetherian local rings. In this paper we enlarge the class of rings known to admit good criteria for finiteness of Gorenstein dimensions: It now includes, for instance, the rings encountered in commutative algebraic geometry and, in the noncommutative realm,
k-algebras with a dualizing complex.
Artinian quotients R of the local ring Q = kx,y,z are classified by multiplicative structures on A = Tor_Q^*(R,k); in particular, R is Gorenstein if and only if A is a Poincare duality algebra while ...R is Golod if and only if all products in A_{>0} are trivial. There is empirical evidence that generic quotient rings with small socle ranks fall on a spectrum between Golod and Gorenstein in a very precise sense: The algebra A breaks up as a direct sum of a Poincare duality algebra P and a graded vector space V, on which P_{>0} acts trivially. That is, A is a trivial extension, A = P \ltimes V, and the extremes A = (k \oplus \Sigma k) \ltimes V and A = P correspond to R being Golod and Gorenstein, respectively. We prove that this observed behavior is, indeed, the generic behavior for graded quotients R of socle rank 2, and we show that the rank of P is controlled by the difference between the order and the degree of the socle polynomial of R.
Every projective module is flat. Conversely, every flat module is a direct limit of finitely generated free modules; this was proved independently by Govorov and Lazard in the 1960s. In this paper we ...prove an analogous result for complexes of modules, and as applications we reprove some results due to Enochs and García Rozas and to Neeman.
Ideals in the ring of power series in three variables can be classified based on algebra structures on their minimal free resolutions. The classification is incomplete in the sense that it remains ...open which algebra structures actually occur; this realizability question was formally raised by Avramov in 2012. We discuss the outcomes of an experiment performed to shed light on Avramov's question: Using the computer algebra system Macaulay2, we classify a billion randomly generated ideals and build a database with examples of ideals of all classes realized in the experiment. Based on the outcomes, we discuss the status of recent conjectures that relate to the realizability question.
Cities and city regions are on the global agenda as key sites for contemporary societal development, in terms of agglomeration of economic activity, places of everyday life and dense networks. The ...majority of economic, political and social activities is today formed by urbanisation, and an increasing number of people are living and working in city regions. At the same time, many cities and peripheral regions are struggling with job losses, industrial restructuring and depopulation, and thus, many countries face new forms of spatially economic and social inequalities. This special issue is about the contemporary urbanisation processes and the transformation of cities and urban systems in the European context using Denmark as a particular case. Denmark provides a present-day example of urban transformation, and its urban system resembles that of many other European countries - Denmark having one large urban centre and a long tail of smaller cities and towns. Thus, the papers in this issue provide insights into contemporary urban changes.
There is a growing European policy interest in small and medium-sized towns’ (SMSTs) potential to contribute to a more balanced territorial development. National policy in Denmark has only recently ...begun to address SMSTs directly. Often, SMSTs’ development is reduced to either being part of bigger functional urban regions or, in the case of rural areas, hidden behind larger regional development agendas. A key research question is therefore which development paths can we see beyond the growth-decline dichotomy. On the backdrop of this, the ESPON TOWN DENMARK project (2022) juxtaposed general trends of growth and decline in population and employment in Danish SMSTs to other aspects as demography, education, industry, service provision as well as regional position. We develop and apply an analytical typology adding more nuances to SMST’s development pathways.
There is a growing European policy interest in small and medium-sized towns’ (SMSTs) potential to contribute to a more balanced territorial development. National policy in Denmark has only recently ...begun to address SMSTs directly. Often, SMSTs’ development is reduced to either being part of bigger functional urban regions or, in the case of rural areas, hidden behind larger regional development agendas. A key research question is therefore which development paths can we see beyond the growth-decline dichotomy. On the backdrop of this, the ESPON TOWN DENMARK project (2022) juxtaposed general trends of growth and decline in population and employment in Danish SMSTs to other aspects as demography, education, industry, service provision as well as regional position. We develop and apply an analytical typology adding more nuances to SMST’s development pathways.
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