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Local Cohomology
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  • Cited by 178
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Aghapournahr, M. Ahmadi-amoli, Kh. and Sadeghi, M. Y. 2017. Cofiniteness and Artinianness of certain local cohomology modules. Ricerche di Matematica, Vol. 65, Issue. 1, p. 21.


    Bahmanpour, Kamal and Quy, Pham Hung 2017. Localization at countably infinitely many prime ideals and applications. Journal of Algebra and Its Applications, Vol. 15, Issue. 03, p. 1650045.


    Bahmanpour, Kamal and Aghapournahr, Moharram 2017. A Note on Cofinite Modules. Communications in Algebra, Vol. 44, Issue. 9, p. 3683.


    Bandari, Somayeh and Jafari, Raheleh 2017. On certain equidimensional polymatroidal ideals. Manuscripta Mathematica, Vol. 149, Issue. 1-2, p. 223.


    Dung, Le Xuan and Hoa, Le Tuan 2017. Dependence of Hilbert coefficients. Manuscripta Mathematica, Vol. 149, Issue. 1-2, p. 235.


    Ghasemi, Ghader Bahmanpour, Kamal and A’zami, Jafar 2017. On the cofiniteness of Artinian local cohomology modules. Journal of Algebra and Its Applications, Vol. 15, Issue. 04, p. 1650070.


    Hamedi-Mobarra, Leila Hassanzadeh-lelekaami, Dawood and Roshan-Shekalgourabi, Hajar 2017. A graph over the commutative rings. Boletín de la Sociedad Matemática Mexicana,


    Morales, Marcel and Dung, Nguyen Thi 2017. Castelnuovo–Mumford regularity and Segre–Veronese transform. Journal of Algebra and Its Applications, Vol. 15, Issue. 06, p. 1650116.


    Puthenpurakal, Tony J. 2017. Associated primes of local cohomology modules over regular rings. Pacific Journal of Mathematics, Vol. 282, Issue. 1, p. 233.


    Rahmati-Asghar, Rahim and Moradi, Somayeh 2017. On the Stanley–Reisner ideal of an expanded simplicial complex. Manuscripta Mathematica, Vol. 150, Issue. 3-4, p. 533.


    Roshan-Shekalgourabi, H. and Hassanzadeh-Lelekaami, D. 2017. On the generalized local cohomology of minimax modules. Journal of Algebra and Its Applications, Vol. 15, Issue. 08, p. 1650147.


    Sahandi, P. Shirmohammadi, N. and Sohrabi, S. 2017. Cohen–Macaulay and Gorenstein Properties under the Amalgamated Construction. Communications in Algebra, Vol. 44, Issue. 3, p. 1096.


    Zamani, N. Bijan-Zadeh, M. H. and Sayedsadeghi, M. S. 2017. Cohomology with support of dimension ≤ d. Journal of Algebra and Its Applications, Vol. 15, Issue. 03, p. 1650042.


    Àlvarez Montaner, Josep 2017. Lyubeznik Table of Sequentially Cohen–Macaulay Rings. Communications in Algebra, Vol. 43, Issue. 9, p. 3695.


    Asadollahi, Davood and Naghipour, Reza 2017. Faltings’ Local-Global Principle for the Finiteness of Local Cohomology Modules. Communications in Algebra, Vol. 43, Issue. 3, p. 953.


    Bahmanpour, Kamal Naghipour, Reza and Sedghi, Monireh 2017. Cofiniteness with Respect to Ideals of Small Dimensions. Algebras and Representation Theory, Vol. 18, Issue. 2, p. 369.


    Bahmanpour, Kamal 2017. Annihilators of Local Cohomology Modules. Communications in Algebra, Vol. 43, Issue. 6, p. 2509.


    Doustimehr, Mohammad Reza and Naghipour, Reza 2017. Faltings' Local-Global Principle for the Minimaxness of Local Cohomology Modules. Communications in Algebra, Vol. 43, Issue. 2, p. 400.


    Fathi, Ali Tehranian, Abolfazl and Zakeri, Hossein 2017. Filter Regular Sequences and Generalized Local Cohomology Modules. Bulletin of the Malaysian Mathematical Sciences Society, Vol. 38, Issue. 2, p. 467.


    Mehrvarz, Ali Akbar Naghipour, Reza and Sedghi, Monireh 2017. Faltings’ Local-global Principle for the Finiteness of Local Cohomology Modules over Noetherian Rings. Communications in Algebra, Vol. 43, Issue. 11, p. 4860.


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    Local Cohomology
    • Online ISBN: 9780511629204
    • Book DOI: https://doi.org/10.1017/CBO9780511629204
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Book description

This book provides a careful and detailed algebraic introduction to Grothendieck's local cohomology theory, and provides many illustrations of applications of the theory in commutative algebra and in the geometry of quasi-affine and quasi-projective varieties. Topics covered include Castelnuovo–Mumford regularity, the Fulton–Hansen connectedness theorem for projective varieties, and connections between local cohomology and both reductions of ideals and sheaf cohomology. It is designed for graduate students who have some experience of basic commutative algebra and homological algebra, and also for experts in commutative algebra and algebraic geometry.

Reviews

‘… a careful and detailed algebraic introduction to Grothendieck’s local cohomology theory.’

Source: L’Enseignment Mathématique

‘The book is well organised, very nicely written, and reads very well … a very good overview of local cohomology theory.’

Source: European Mathematical Society

‘I am sure that this will be a standard text and reference book for years to come.’

Liam O’Carroll Source: Bull. London Mathematical Society

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