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Local Cohomology
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  • Cited by 224
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Rezaei, Shahram 2018. $${\varvec{\mathcal {S}}}$$S-minimaxness and local cohomology modules. Archiv der Mathematik, Vol. 110, Issue. 6, p. 563.
    Lotfi Parsa, M. 2018. Bass numbers of generalized local cohomology modules with respect to a pair of ideals. Asian-European Journal of Mathematics, Vol. 11, Issue. 02, p. 1850019.
    An, Tran Nguyen 2018. Some properties of Artinian modules and applications. Journal of Algebra and Its Applications, Vol. 17, Issue. 02, p. 1850019.
    Mousavi, Seyed Ali and Nekooei, Reza 2018. Characterization of Secondary Modules over Dedekind Domains. Iranian Journal of Science and Technology, Transactions A: Science,
    Hernández, Daniel J. Núñez-Betancourt, Luis Pérez, Felipe and Witt, Emily E. 2018. Cohomological dimension, Lyubeznik numbers, and connectedness in mixed characteristic. Journal of Algebra,
    Farokhi, Asghar and Nazari, Alireza 2018. Cofiniteness of Local Cohomology Modules over Homomorphic Image of Cohen-Macaulay Rings. Acta Mathematica Vietnamica, Vol. 43, Issue. 3, p. 565.
    Eghbali, Majid 2018. A note on the use of Frobenius map and D-modules in local cohomology. Communications in Algebra, Vol. 46, Issue. 2, p. 851.
    Nazari, Malyha and Sazeedeh, Reza 2018. Cofiniteness with Respect to Two Ideals and Local Cohomology. Algebras and Representation Theory,
    DAO, HAILONG and QUY, PHAM HUNG 2018. ON THE ASSOCIATED PRIMES OF LOCAL COHOMOLOGY. Nagoya Mathematical Journal, p. 1.
    Bamdad, Hamidreza and Vahidi, Alireza 2018. Extension Functors of Cousin Cohomology Modules. Bulletin of the Iranian Mathematical Society, Vol. 44, Issue. 2, p. 253.
    Rastgoo, Fahimeh and Nazari, Alireza 2018. Some results on the cofiniteness and annihilators of local cohomology modules. Communications in Algebra, Vol. 46, Issue. 7, p. 3164.
    Puthenpurakal, Tony J. and Reddy, Rakesh B. T. 2018. de Rham cohomology of local cohomology modules II. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry,
    Mahdikhani, A. Sahandi, P. and Shirmohammadi, N. 2018. Cohen–Macaulayness of trivial extensions. Journal of Algebra and Its Applications, Vol. 17, Issue. 01, p. 1850008.
    Bahmanpour, Kamal Naghipour, Reza and Sedghi, Monireh 2018. Modules cofinite and weakly cofinite with respect to an ideal. Journal of Algebra and Its Applications, Vol. 17, Issue. 03, p. 1850056.
    Aghapournahr, Moharram 2018. Cofiniteness of local cohomology modules for a pair of ideals for small dimensions. Journal of Algebra and Its Applications, Vol. 17, Issue. 02, p. 1850020.
    Cường, Đoàn Trung Nam, Phạm Hồng and Quý, Phạm Hùng 2018. On the Length Function of Saturations of Ideal Powers. Acta Mathematica Vietnamica,
    Hassani, Feysal and Rasuli, Rasul 2017. Some Properties of Serre Subcategories in the Graded Local Cohomology Modules. Journal of Mathematics, Vol. 2017, Issue. , p. 1.
    Saremi, Hero 2017. A note on graded generalized local cohomology modules. Quaestiones Mathematicae, Vol. 40, Issue. 5, p. 599.
    Pirmohammadi, Gholamreza Ahmadi Amoli, Khadijeh and Bahmanpour, Kamal 2017. Artinian Cofinite Modules and Going-up for R ⊆ R ̂ $R\subseteq \widehat {R}$ . Acta Mathematica Vietnamica, Vol. 42, Issue. 4, p. 605.
    Hassanzadeh-Lelekaami, D. and Roshan-Shekalgourabi, H. 2017. Extension functors of cominimax modules. Communications in Algebra, Vol. 45, Issue. 2, p. 621.
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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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