Little dimension and the improved new intersection theorem
DOI:
https://doi.org/10.7146/math.scand.a-119740Abstract
Let $R$ be a commutative noetherian local ring. We define a new invariant for $R$-modules which we call the little dimension. Using it, we extend the improved new intersection theorem.
References
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Bruns, W. and Herzog, J., Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics, vol. 39, Cambridge University Press, Cambridge, 1993.
Christensen, L. W., Gorenstein dimensions, Lecture Notes in Mathematics, vol. 1747, Springer-Verlag, Berlin, 2000. https://doi.org/10.1007/BFb0103980
Evans, E. G. and Griffith, P., The syzygy problem, Ann. of Math. (2) 114 (1981), no. 2, 323–333. https://doi.org/10.2307/1971296
Foxby, H.-B., Bounded complexes of flat modules, J. Pure Appl. Algebra 15 (1979), no. 2, 149–172. https://doi.org/10.1016/0022-4049(79)90030-6
Foxby, H.-B. and Iyengar, S., Depth and amplitude for unbounded complexes, in “Commutative algebra (Grenoble/Lyon, 2001)”, Contemp. Math., vol. 331, Amer. Math. Soc., Providence, RI, 2003, pp. 119–137. https://doi.org/10.1090/conm/331/05906
Foxby, H.-B. and Yassemi, S., Small dimension and intersection theorem (infinite version), private notes, 1999.
Hartshorne, R., Residues and duality, Lecture Notes in Mathematics, no. 20, Springer-Verlag, Berlin-New York, 1966.
Heitmann, R. and Ma, L., Big Cohen-Macaulay algebras and the vanishing conjecture for maps of Tor in mixed characteristic, Algebra Number Theory 12 (2018), no. 7, 1659–1674. https://doi.org/10.2140/ant.2018.12.1659
Hochster, M., Canonical elements in local cohomology modules and the direct summand conjecture, J. Algebra 84 (1983), no. 2, 503–553. https://doi.org/10.1016/0021-8693(83)90092-3
Hochster, M., Homological conjectures, old and new, Illinois J. Math. 51 (2007), no. 1, 151–169.
Iyengar, S., Depth for complexes, and intersection theorems, Math. Z. 230 (1999), no. 3, 545–567. https://doi.org/10.1007/PL00004705
Sharif, T. and Yassemi, S., Special homological dimensions and intersection theorem, Math. Scand. 96 (2005), no. 2, 161–168. https://doi.org/10.7146/math.scand.a-14950
Sharp, R. Y., Cohen-Macaulay properties for balanced big Cohen-Macaulay modules, Math. Proc. Cambridge Philos. Soc. 90 (1981), no. 2, 229–238. https://doi.org/10.1017/S0305004100058680
Veliche, O., Construction of modules with finite homological dimensions, J. Algebra 250 (2002), no. 2, 427–449. https://doi.org/10.1006/jabr.2001.9100
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Published
2020-05-06
How to Cite
Nakamura, T., Takahashi, R., & Yassemi, S. (2020). Little dimension and the improved new intersection theorem. MATHEMATICA SCANDINAVICA, 126(2), 209–220. https://doi.org/10.7146/math.scand.a-119740
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