Abstract

The Boij-Soderberg conjectures describe the rational cone of Betti diagrams of Cohen-Macaulay modules. We explain these conjectures and how they have been settled. The first conjectures the existence of pure resolutions. We give two constructions of such resolutions. The second conjectures that the Betti diagrams of pure resolutions give all the extremal rays in the rational cone of Betti diagrams. We indicate how this has been proven.



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