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Derived Equivalences for Group Rings

✍ Scribed by Steffen König, Alexander Zimmermann (auth.)

Book ID
127418343
Publisher
Springer
Year
1998
Tongue
English
Weight
2 MB
Edition
1
Category
Library
City
Berlin; New York
ISBN
3540697489
ISSN
0075-8434

No coin nor oath required. For personal study only.

✦ Synopsis

A self-contained introduction is given to J. Rickard's Morita theory for derived module categories and its recent applications in representation theory of finite groups. In particular, Broué's conjecture is discussed, giving a structural explanation for relations between the p-modular character table of a finite group and that of its "p-local structure". The book is addressed to researchers or graduate students and can serve as material for a seminar. It surveys the current state of the field, and it also provides a "user's guide" to derived equivalences and tilting complexes. Results and proofs are presented in the generality needed for group theoretic applications.

✦ Subjects

K-Theory

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Equivalences of comodule categories for
Equivalences of comodule categories for coalgebras over rings
✍ Khaled Al-Takhman 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 260 KB

In this article we deÿned and studied quasi-ÿnite comodules, the cohom functors for coalgebras over rings. Linear functors between categories of comodules are also investigated and it is proved that good enough linear functors are nothing but a cotensor functor. Our main result of this work characte