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- W2891811760 abstract "Let R denote a commutative ring and (mathfrak {a}) an ideal of R. The (mathfrak {a})-torsion functor and the (mathfrak {a})-completion functor, defined respectively by (varGamma _{mathfrak {a}}(M):= {min M mid mathfrak {a}^t m=0 text { for some } tin mathbb {N}}) and (varLambda ^{mathfrak a}(M):= varprojlim (R/mathfrak {a}^t otimes _R M)) for any R-module M, extends naturally to complexes. In this chapter we first recall that (mathrm{L} varLambda ^{mathfrak a}) and (mathrm{R} varGamma _{mathfrak a}) are well defined in the derived category and fix some notations. Then we investigate when (mathrm{L} varLambda ^{mathfrak a}(X)) and (mathrm{R} varGamma _{mathfrak a}(X)) vanish. For complexes homologically-bounded on the good size we obtain more precise results, previously known when the ring is Noetherian, possibly new in the present generality. We also provide a description of (mathrm{L} varLambda ^{mathfrak a}(X)) and (mathrm{R} varGamma _{mathfrak a}(X)) in terms of microscope and telescope. These descriptions do not refer to the resolutions of X, which could be an advantage." @default.
- W2891811760 created "2018-09-27" @default.
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- W2891811760 date "2018-01-01" @default.
- W2891811760 modified "2023-09-27" @default.
- W2891811760 title "Local Cohomology and Local Homology" @default.
- W2891811760 doi "https://doi.org/10.1007/978-3-319-96517-8_7" @default.
- W2891811760 hasPublicationYear "2018" @default.
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