Local Cohomology
Grothendieck's local cohomology and its applications to depth and connectivity.
Local Cohomology. Grothendieck’s local cohomology and its applications to depth and connectivity.
Foundations and canonical references
The standard treatments of local cohomology approach the subject from complementary angles. Brodmann, Local Cohomology: An Algebraic Introduction with Geometric Applications (2013) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Iyengar, Twenty-Four Hours of Local Cohomology (2007) offers an alternative presentation that complements the primary references and is useful for triangulating definitions and proof techniques.
Open methodological questions for local cohomology include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2013Local Cohomology: An Algebraic Introduction with Geometric Applicationsbrodmann-2013, sharp-2013
- textbook · supporting · 2007Twenty-Four Hours of Local Cohomologyiyengar-2007
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