Title
Representations Of Finite Groups: Local Cohomology And Support (Oberwolfach Seminars, 43)
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The Seminar Focuses On A Recent Solution, By The Authors, Of A Long Standing Problem Concerning The Stable Module Category (Of Not Necessarily Finite Dimensional Representations) Of A Finite Group. The Proof Draws On Ideas From Commutative Algebra, Cohomology Of Groups, And Stable Homotopy Theory. The Unifying Theme Is A Notion Of Support Which Provides A Geometric Approach For Studying Various Algebraic Structures. The Prototype For This Has Been Daniel Quillens Description Of The Algebraic Variety Corresponding To The Cohomology Ring Of A Finite Group, Based On Which Jon Carlson Introduced Support Varieties For Modular Representations. This Has Made It Possible To Apply Methods Of Algebraic Geometry To Obtain Representation Theoretic Information. Their Work Has Inspired The Development Of Analogous Theories In Various Contexts, Notably Modules Over Commutative Complete Intersection Rings And Over Cocommutative Hopf Algebras. One Of The Threads In This Development Has Been The Classification Of Thick Or Localizing Subcategories Of Various Triangulated Categories Of Representations. This Story Started With Mike Hopkins Classification Of Thick Subcategories Of The Perfect Complexes Over A Commutative Noetherian Ring, Followed By A Classification Of Localizing Subcategories Of Its Full Derived Category, Due To Amnon Neeman. The Authors Have Been Developing An Approach To Address Such Classification Problems, Based On A Construction Of Local Cohomology Functors And Support For Triangulated Categories With Ring Of Operators. The Book Serves As An Introduction To This Circle Of Ideas.
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- Q: What is the page count of this book? A: This book contains one hundred fifteen pages. It provides a comprehensive introduction to local cohomology and support in finite groups.
- Q: What are the dimensions of this book? A: The book measures six point seventy-five inches in length, zero point twenty-five inches in width, and nine point seventy-six inches in height.
- Q: What type of binding does this book have? A: This book is available in paperback binding. The paperback format makes it lightweight and easy to handle.
- Q: Who is the author of this book? A: The author of this book is David J. Benson. He is known for his contributions to the field of mathematics, particularly in representation theory.
- Q: What category does this book fall under? A: This book is categorized under Abstract. It discusses complex mathematical concepts related to finite groups.
- Q: How do I read this book effectively? A: To read this book effectively, it’s best to have a background in algebra and cohomology. This will help you grasp the advanced concepts discussed.
- Q: Is this book suitable for beginners in mathematics? A: No, this book is not suitable for beginners. It is intended for readers with a solid understanding of advanced algebra and representation theory.
- Q: Can I use this book for self-study? A: Yes, you can use this book for self-study. It serves as an introduction to complex ideas in local cohomology, though prior knowledge is recommended.
- Q: How should I store this book? A: Store this book in a cool, dry place away from direct sunlight. This will help maintain its condition over time.
- Q: Are there any specific care instructions for this book? A: No specific care instructions are needed. However, handling it gently and keeping it away from moisture will help preserve its quality.
- Q: What if the book arrives damaged? A: If the book arrives damaged, you should contact the seller for a return or exchange. Most sellers have a policy for damaged goods.
- Q: Can I return this book if I don't find it useful? A: Yes, you can typically return this book if it is in its original condition, but check the seller's return policy for specifics.
- Q: Is this book a good resource for research? A: Yes, this book is a valuable resource for research in algebra and representation theory. It offers in-depth discussions and recent findings.
- Q: Does this book include references for further reading? A: Yes, this book includes references for further reading. It guides readers to additional resources on the topics discussed.
- Q: Is this book part of a series? A: Yes, this book is part of the Oberwolfach Seminars series. This series focuses on various advanced topics in mathematics.