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Journal of the London Mathematical Society Advance Access originally published online on April 7, 2008
Journal of the London Mathematical Society 2008 78(1):85-106; doi:10.1112/jlms/jdn013
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© 2008 London Mathematical Society

Graded Betti numbers of Cohen–Macaulay modules and the multiplicity conjecture

Mats Boij and Jonas Söderberg

Department of Mathematics
Royal Institute of Technology
S–100 44 Stockholm
Sweden
boij@math.kth.se

We give conjectures on the possible graded Betti numbers of Cohen–Macaulay modules up to multiplication by positive rational numbers. The idea is that the Betti diagrams should be non-negative linear combinations of pure diagrams. The conjectures are verified in the cases where the structure of resolutions is known, that is: for modules of codimension two, for Gorenstein algebras of codimension three and for complete intersections. The motivation for proposing the conjectures comes from the Multiplicity conjecture of Herzog, Huneke and Srinivasan.

2000 Mathematics Subject Classification 13C14.

Received March 6, 2007; published online April 7, 2008.


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