Vanishing of Tor, and why we care about it

• Olgur Celikbas ^[1] ; Roger Wiegand ^[2]
  1. [1] University of Missouri

     University of Missouri

     Township of Columbia, Estados Unidos

     
  2. [2] University of Nebraska–Lincoln

     University of Nebraska–Lincoln

     Estados Unidos

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 3 ((March 2015)), 2015 (Ejemplar dedicado a: Special Issue in honor of Prof. Hans-Bjørn Foxby), págs. 429-448
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.05.003
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• Resumen

  • Given finitely generated modules M and N over a local ring R , the tensor product M⊗RNM⊗RN typically has nonzero torsion. Indeed, the assumption that the tensor product is torsion-free influences the structure and vanishing of the modules ToriR(M,N) for all i≥1i≥1. In turn, the vanishing of ToriR(M,N) imposes restrictions on the depth properties of the modules M and N. These connections made their first appearance in Auslander's 1961 paper “Modules over unramified regular local rings”. We will survey the literature on these topics, with emphasis on progress during the past twenty years.