1. Homological preliminaries 2. Adic topologies and completions 3. Injective envelopes and minimal injective resolutions 4. Local cohomology and koszul complexes 5. (Pre-) Regular sequences and depth 6. Exactness of complexes and linear equations over rings 7. Comparing homological invariants 8. Dimensions 9. Cohen-Macauley modules and regular rings 10. Gorenstein rings, local duality, and the direct summand conjecture 11. Frobenius and big Cohen-Macauley modules 12. Big Cohen-Macaulay modules in equal charecteristic 0 13. Uses of big Cohen-Maculay Modules.
1. Homological preliminaries 2. Adic topologies and completions 3. Injective envelopes and minimal injective resolutions 4. Local cohomology and koszul complexes 5. (Pre-) Regular sequences and depth 6. Exactness of complexes and linear equations over rings 7. Comparing homological invariants 8. Dimensions 9. Cohen-Macauley modules and regular rings 10. Gorenstein rings, local duality, and the direct summand conjecture 11. Frobenius and big Cohen-Macauley modules 12. Big Cohen-Macaulay modules in equal charecteristic 0 13. Uses of big Cohen-Maculay Modules.
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