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Local Cohomology
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  • Cited by 208
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    This (lowercase (translateProductType product.productType)) has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Hassani, Feysal and Rasuli, Rasul 2017. Some Properties of Serre Subcategories in the Graded Local Cohomology Modules. Journal of Mathematics, Vol. 2017, 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.

    Banisaeed, E. Rahmati, F. Ahmadi-Amoli, Kh. and Eghbali, M. 2017. On the relation between formal grade and depth with a view toward vanishing of Lyubeznik numbers. Communications in Algebra, Vol. 45, Issue. 12, p. 5137.

    Ma, Linquan Schwede, Karl and Shimomoto, Kazuma 2017. Local cohomology of Du Bois singularities and applications to families. Compositio Mathematica, Vol. 153, Issue. 10, p. 2147.

    Mohammadi Aghjeh Mashhad, Fatemeh 2017. Gorenstein homological dimensions and some duality results. Asian-European Journal of Mathematics, Vol. 10, Issue. 03, p. 1750048.

    Rahmani, Mohammad and Taherizadeh, Abdoljavad 2017. Characterizing local rings via perfect and coperfect modules. Journal of Algebra and Its Applications, Vol. 16, Issue. 04, p. 1750066.

    Bahmanpour, Kamal 2017. A note on Lynch’s conjecture. Communications in Algebra, Vol. 45, Issue. 6, p. 2738.

    Hamedi-Mobarra, Leila Hassanzadeh-lelekaami, Dawood and Roshan-Shekalgourabi, Hajar 2017. A graph over the commutative rings. Boletín de la Sociedad Matemática Mexicana, Vol. 23, Issue. 2, p. 611.


    Yoshizawa, Takeshi 2017. On the closedness of taking injective hulls of several Serre subcategories. Communications in Algebra, Vol. 45, Issue. 11, p. 4846.

    Rahmani, Mohammad and Taherizadeh, Abdoljavad 2017. Dual of bass numbers and dualizing modules. Communications in Algebra, Vol. 45, Issue. 4, p. 1493.


    Eghbali, Majid 2017. A note on the use of Frobenius map and D-modules in local cohomology. Communications in Algebra, p. 1.

    Walther, Uli 2017. The Jacobian module, the Milnor fiber, and the D-module generated by $$f^s$$ f s. Inventiones mathematicae, Vol. 207, Issue. 3, p. 1239.

    Rahmani, Mohammad and Taherizadeh, Abdoljavad 2017. Tensor product of C-injective modules. Communications in Algebra,

    Rezaei, Shahram 2017. Some results on top local cohomology and top formal local cohomology modules. Communications in Algebra, Vol. 45, Issue. 5, p. 1935.

    Thompson, Peder 2017. Stable local cohomology. Communications in Algebra, Vol. 45, Issue. 1, p. 198.

    Rahimpour Nasbi, Yashar Vahidi, Alireza and Ahmadi Amoli, Khadijeh 2017. Torsion functors of generalized local cohomology modules. Communications in Algebra, Vol. 45, Issue. 12, p. 5420.

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    Local Cohomology
    • Online ISBN: 9780511629204
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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.


‘… 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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