Derived category of squarefree modules and local cohomology with monomial ideal support

@article{Yanagawa2003DerivedCO,
  title={Derived category of squarefree modules and local cohomology with monomial ideal support},
  author={Kohji Yanagawa},
  journal={Journal of The Mathematical Society of Japan},
  year={2003},
  volume={56},
  pages={289-308}
}
  • Kohji Yanagawa
  • Published 10 March 2003
  • Mathematics
  • Journal of The Mathematical Society of Japan
A "squarefree module" over a polynomial ring $S = k[x_1, .., x_n]$ is a generalization of a Stanley-Reisner ring, and allows us to apply homological methods to the study of monomial ideals systematically. Let $Sq$ be the category of squarefree modules. Then the derived category $D^b(Sq)$ of $Sq$ has three duality functors which act on $D^b(Sq)$ just like three transpositions of the symmetric group $S_3$ (up to translation). This phenomenon is closely related to the Koszul dulaity (in particular… 
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  • Kohji Yanagawa
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 2001
In this paper, we will study the local cohomology modules HiI(S) of a polynomial ring S = k[x1, …, xn] with supports in a (radical) monomial ideal I. When S/I is a Cohen–Macaulay ring of dimension d
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