- The conjectures
- Origins and statements, [H1], [HZ], [HZ2]
- Resolutions and syzygies
- Resolutions and finitistic dimension for monomial algebras,
[AG, sections 1 and 2], [GKK, Corollary 2.5]
- Finite finitistic dimension for radical
cubed 0 and generalisations, [W]
- Resolutions in general, [GSZ, sections 1
and 2], [BK, section 7]
- Gröbner bases, [E], [G1, (G2)]
- Homologically finite subcategories
- Basic definitions and examples, [AR1,
section 1], [AR2, Corollary 1.8], [AS,
Theorem 4.5, Proposition 4.6]
- Contravariant finiteness for the modules
of finite projective dimension, [AR1,
Corollary 3.10], [IST]
- Torsion theories and tilting modules,
[A, section 1]
- Correspondence between (co)tilting
modules and special homologically finite
subcategories, [A, Theorem 3.2], [AR1,
Theorem 5.5]
- Representation dimension
- Representation dimension of artin
algebras, [Au, Chapter III], [X1, X2]
- Geometric aspects
- Varieties of algebras and modules, [MHS,
section 1], [G, Lemma 3.2]
- Bounds for global and finistic
dimensions, [MHS, section 2, 3]
- Commutative theory
- The Auslander-Buchsbaum formula, [BH, Theorem 1.3.3]
- Characterisations of regular local rings, [BH, Theorem 2.2.7]
- Characterisations of complete
intersections, [BH, section 2.3]
- Finitistic dimension equals Krull
dimension, [GR, section 3.2] and [B,
Corollary 5.5]
- Infinitely generated modules
- The difference between the little and the
big finitistic dimension, [S]
- Criteria for equality of the little and the big
finitistic dimension, [HZS], [Kr]
- Contravariant finiteness for the modules
of projective dimension less than n,
[AEJO], [KS]
- Derived categories
- Introduction to derived categories and
tilting, [H3], [K1], [K2], [K3]
- Reduction techniques for homological conjectures, [H2]
References for the papers
listed above.
Distribution of the
lectures in the first part.
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