An Introduction to Mathematical Reasoning. Home Contact Us Help Free delivery worldwide. Contents The local cohomology functors. Applications to reductions of ideals. The Annihilator and Finiteness Theorems. The Mayer-Vietoris sequence; 4.
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The local cohomology functors; 2. Torsion modules and ideal transforms; 3. The Mayer-Vietoris sequence; 4. Change of rings; 5. Other approaches; 6. Fundamental vanishing theorems; 7. Artinian local cohomology modules; 8. The Lichtenbaum-Hartshorne Theorem; 9. The Annihilator and Finiteness Theorems; Matlis duality; Local duality; Canonical modules; Foundations in the graded case; Graded versions of basic theorems; Links with projective varieties; Castelnuovo regularity; Hilbert polynomials; Applications to reductions of ideals; Connectivity in algebraic varieties; Links with sheaf cohomology; Bibliography; Index.
I am sure that this will be a standard text and reference book for years to come. Indeed, it is well written and, overall, almost self-contained, which is very important in a book addressed to graduate students. Boix, Mathematical Reviews "From the point of view of the reviewer who learned all his basic knowledge about local cohomology reading the first edition of this book and doing some of its exercises , the changes previously described the new Chapter 12 concerning canonical modules, the treatment of multigraded local cohomology, and the final new section of Chapter 20 about locally free sheaves definitely make this second edition an even better graduate textbook than the first.
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Local cohomology : an algebraic introduction with geometric applications
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