## Lecture notes

Lecture 0: Overview (

pdf)

Lecture 1: Derived algebraic geometry (

pdf)

Lecture 2: Descent for quasi-coherent sheaves (

pdf)

Lecture 3: Compact generation for quasi-coherent sheaves (

pdf)

Lecture 4: Zariski descent in algebraic K-theory (

pdf)

Lecture 5: The cotangent complex and Nisnevich descent (

pdf)

Lecture 6: Proper morphisms in derived algebraic geometry (

pdf)

Lecture 7: Derived blow-ups (

pdf)

Lecture 8: Pro-systems of K-theory spectra (

pdf)

Lecture 9: Pro cdh excision in K-theory (

pdf)

Lecture 10: Pro Milnor excision in K-theory (

pdf)

*These are preliminary notes; read with caution.*

## References

[KST] Moritz Kerz, Florian Strunk, Georg Tamme,

*Algebraic K-theory and descent for blow-ups*,

arXiv:1611.08466
[L] Jacob Lurie, *Spectral Algebraic Geometry*, pdf

[TT] R.W. Thomason and T. Trobaugh, *Higher algebraic K-theory of schemes and of derived categories*