**RESEARCH IN PAIRS**

**Gorenstein Homological Algebra****June 5 - 16, 2017**
Our project is in Gorenstein homological algebra. The Gorenstein homological methods have proved to be very useful; but they can only be applied when the appropriate resolutions exist. While the classical (injective, projective, flat) resolutions exist over any ring, the question "What is the most general type of ring over which all modules have a Gorenstein projective (injective, flat) resolution?" is still open. Besides considering this question, we want to develop a theory of Gorenstein homological algebra in categories of sheaves, a theory with good local-global transfer properties, characterize Gorenstein rings via unbounded complexes, and find conditions on a bicomplete abelian category with enough projectives and injectives such that the categories of Gorenstein projective and injective objects are Quillen equivalent. The methods: we will use various recently developed techniques in homological algebra of complexes, as well as methods from triangulated categories. |
ParticipantsSergio Estrada (University of Murcia) Alina Jacob (Georgia Southern University) Marco Perez (National Autonomous University of Mexico) Sponsor |