Preface

Fine and coarse moduli spaces in the representation theory of finite dimensional algebras

1. Introduction and notation

Acknowledgements

2. Affine and projective parametrizations of the Λ-modules of dimension vector 𝐝

3. Quotient varieties on the geometric market—generalities and representation-theoretic particulars

4. Rendering Riemann’s classification philosophy more concrete

5. Approach A: King’s adaptation of Mumford stability: Focusing on the objects which are (semi-)stable relative to a weight function

6. Approach B. Slicing Λ-𝑚𝑜𝑑 into strata with fixed top

7. Slicing Λ-𝑚𝑜𝑑 more finely, in terms of radical layerings Representation-theoretically optimal coordinatization of 𝔊𝔯𝔞𝔰𝔰^{𝔗}_{𝐝}

8. Problems. Pros and Cons of Approach B

References

More Representations of Wild Quivers

Introduction

1. Preliminaries

2. Spectral properties of the Coxeter transformations

3. Elementary modules

4. The regular components

5. Partial tilting modules

6. The perpendicular category of a rigid regular module

7. A functor between categories of regular modules

8. Generation of cocones

9. Factorisations of morphisms

References

Phantom Morphisms and Salce’s Lemma

1. Introduction

2. Preliminaries

3. Salce’s Lemma

4. The Flat Cover Conjecture

5. Phantom Morphisms

6. Salce’s Lemma for Ideals

7. Subfunctors of 𝐸𝑥𝑡

8. Examples

9. Quasi-Frobenius Rings

10. The Powers of the Phantom Ideal

References

Morita theory, revisited

1. Introduction

2. Notations

3. Morita theory

4. The Lambek theorem

5. Self-dual idempotents and Morita algebras

References

Universal deformation rings of group representations, with an application of Brauer’s generalized decomposition numbers

1. Introduction

2. Mazur’s deformation theory

3. Universal deformation rings of modules for finite groups

4. Brauer’s generalized decomposition numbers and universal deformation rings

References

Derived Representation Schemes and Noncommutative Geometry

1. Introduction

Notation and Conventions

2. Model categories

3. Representation Schemes

4. Cyclic Homology and Higher Trace Maps

5. Abelianization of the Representation Functor

6. Examples

Acknowledgements

References

Classifying torsion pairs for tame hereditary algebras and tubes

Introduction

1. Torsion pairs

2. Torsion pairs and tilting for finite dimensional algebras

3. Big cotilting modules for finite dimensional algebras

4. Tubes

5. Combinatorial classifications

References

Problems solved by using degrees of irreducible morphisms

Introduction

1. Preliminaries and Notation

2. On degrees

3. Characterizations of the notion of degree

4. Composite of irreducible morphisms and the powers of the radical of a module category

5. Degrees and finite representation type of an algebra

6. On the bound of the radical of a module category

References

Arc diagram varieties

1. Introduction

Acknowledgement

2. The stratification

3. Partially ordered sets

4. An algorithmic approach

5. Three excursions

References