Descent in algebraic K-theory

Time and place

Wintersemester 2017/18
Mondays 14-16, SFB seminar room

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