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Multiplicities and Chern Classes in Local Algebra
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    Dao, Hailong De Stefani, Alessandro Grifo, Eloísa Huneke, Craig and Núñez-Betancourt, Luis 2018. Singularities and Foliations. Geometry, Topology and Applications. Vol. 222, Issue. , p. 387.

    Walker, Mark 2017. Total Betti numbers of modules of finite projective dimension. Annals of Mathematics, Vol. 186, Issue. 2, p. 641.

    Chan, C.-Y. Jean and Kurano, Kazuhiko 2016. Hilbert–Kunz Functions over Rings Regular in Codimension One. Communications in Algebra, Vol. 44, Issue. 1, p. 141.

    Budur, Nero and Wang, Botong 2015. Cohomology jump loci of differential graded Lie algebras. Compositio Mathematica, Vol. 151, Issue. 08, p. 1499.

    Kurano, Kazuhiko and Ohta, Kosuke 2015. On the Limit of Frobenius in the Grothendieck Group. Acta Mathematica Vietnamica, Vol. 40, Issue. 1, p. 161.

    Yousefian Darani, Ahmad and Motmaen, Shahram 2013. Zariski topology on the spectrum of graded classical prime submodules. Applied General Topology, Vol. 14, Issue. 2,

    Colomé-Nin, Gemma and Elias, Juan 2011. On the Asymptotic Depth of Multigraded Modules. Communications in Algebra, Vol. 39, Issue. 9, p. 3298.

    Chinburg, Ted Pappas, Georgios and Taylor, Martin 2009. Cubic structures, equivariant Euler characteristics and lattices of modular forms. Annals of Mathematics, Vol. 170, Issue. 2, p. 561.

    Logvinenko, Timothy 2008. Derived McKay correspondence via pure-sheaf transforms. Mathematische Annalen, Vol. 341, Issue. 1, p. 137.

    Chan, C.-Y. Jean and Huang, I.-Chiau 2007. Module Structure of an Injective Resolution. Communications in Algebra, Vol. 35, Issue. 11, p. 3713.

    Avramov, Luchezar L. Buchweitz, Ragnar-Olaf and Iyengar, Srikanth 2007. Class and rank of differential modules. Inventiones mathematicae, Vol. 169, Issue. 1, p. 1.

    Brenner, Holger and Schröer, Stefan 2003. Ample families, multihomogeneous spectra, and algebraization of formal schemes. Pacific Journal of Mathematics, Vol. 208, Issue. 2, p. 209.

    Kurano, Kazuhiko 2001. Geometric And Combinatorial Aspects Of Commutative Algebra.

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    Multiplicities and Chern Classes in Local Algebra
    • Online ISBN: 9780511529986
    • Book DOI: https://doi.org/10.1017/CBO9780511529986
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Book description

The theory of local Chern characters used in commutative algebra originated in topology some years ago, and from there was introduced in algebraic geometry. This book describes the theory in an algebraic setting, presenting research results and important algebraic applications, some of which come from the author's own work. It concentrates on the background in commutative algebra and homological algebra and describes the relations between these subjects, including extensive discussions of the homological conjectures and of the use of the Frobenius map.

Reviews

Review of the hardback:‘… a well-motivated survey of such a broad range of material, some of it quite technical, which leads the reader to the forefront of some of the deepest modern developments in Intersection Theory.’

Source: Proceedings of the Edinburgh Mathematical Society

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