日 時： 平成19年5月9日(水)午後4時から5時まで
場 所： 理学部C棟3階C３０９
講演者： Lars Winther Christensen (University of Nebraska-Lincoln)
題 目： How to detect finiteness of Gorenstein homological dimensions
内 容： It is a maxim in ring theory that understanding a ring is tantamount to understanding its modules. One way of analyzing a given module is to approximate it by modules that are already well-understood. This idea leads to the concept of homological dimensions. A classical example is approximation by free modules, which leads to the concept of projective dimension. A module has finite homological dimension if an approximation can be achieved in finitely many steps; experience shows that such modules have special properties. Hence, it becomes important to detect if a given module has finite homological dimension, possibly without having to construct an approximation. Experience points to vanishing of (co)homology as a detection mechanism. For a family of dimensions, known as Gorenstein homological dimensions, such an alternative way to detect finiteness has long been sought. I will survey the background for this problem and describe a solution that works for the rings encountered in algebraic geometry.
