# 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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