TY - JOUR
T1 - A local duality principle in derived categories of commutative Noetherian rings
AU - Nakamura, Tsutomu
AU - Yoshino, Yuji
N1 - Funding Information:
This work was finished during the first author's visit to the Department of Mathematics at the University of Utah supported by a research grant from Research Institute for Interdisciplinary Science at Okayama University. We are grateful to Srikanth Iyengar for his helpful comments, which improve many parts of this paper. We would also like to thank the referee for his/her careful reading. The second author was supported by JSPS Grant-in-Aid for Scientific Research 26287008 .
Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2018/9
Y1 - 2018/9
N2 - Let R be a commutative Noetherian ring. We introduce the notion of colocalization functors γW with supports in arbitrary subsets W of Spec R. If W is a specialization-closed subset, then γW coincides with the right derived functor RΓW of the section functor ΓW with support in W. We prove that the local duality theorem and the vanishing theorem of Grothendieck type hold for γW with W being an arbitrary subset.
AB - Let R be a commutative Noetherian ring. We introduce the notion of colocalization functors γW with supports in arbitrary subsets W of Spec R. If W is a specialization-closed subset, then γW coincides with the right derived functor RΓW of the section functor ΓW with support in W. We prove that the local duality theorem and the vanishing theorem of Grothendieck type hold for γW with W being an arbitrary subset.
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U2 - 10.1016/j.jpaa.2017.10.008
DO - 10.1016/j.jpaa.2017.10.008
M3 - Article
AN - SCOPUS:85031694327
SN - 0022-4049
VL - 222
SP - 2580
EP - 2595
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 9
ER -