Math 662 Course Notes

For derived categories:
References are Weibel, Chapter 10, and/or the MSRI Publication by Yekutieli, Introduction to derived categories, arxiv version arxiv.org/pdf/1501.06731.

For Koszul algebras:
A reference is Section 3.4 of the Hochschild cohomology book linked below.

For products on cohomology:
A reference is Sections 2.1 and 2.2 of the Hochschild cohomology book linked below. (These sections are written specifically for Hochschild cohomology, but the ideas are general, as discussed in class.)

For an introduction to Hochschild cohomology, smooth algebras, Van den Bergh duality, and Calabi Yau algebras:
Instead of course notes, a reference is the book Hochschild Cohomology for Algebras, available at https://www.tamu.edu/~sjw/pub/gsm204.pdf, Sections 1.1, 1.2, 4.1, and 4.3.

Latest version of Course Notes:
Notes 27 March 2025 (Small edits to Sections 7, 8, and 9. Bar resolution for group cohomology added to Section 9.)

Old versions:
Notes 21 March 2025

Notes 19 March 2025

Notes 7 March 2025

Notes 3 March 2025

Notes 26 February 2025

Notes 12 February 2025

Notes 10 February 2025

Notes 6 February 2025

Notes 29 January 2025

Notes 23 January 2025

Notes 17 January 2025

Notes 15 January 2025