Abstract
For t in Nn, E. Miller has defined a category of positively t-determined modules over the polynomial ring S in n variables. We consider the Auslander–Reiten translate, Nt, on the (derived) category of such modules. A monomial ideal I is t-determined if each generator xa has a⩽t. We compute the multigraded cohomology and Betti spaces of Ntk(S/I) for every iterate k and also the S-module structure of these cohomology modules. This comprehensively generalizes results of Hochster and Gräbe on local cohomology of Stanley–Reisner rings.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.