Reading seminar of Algebraic K-theory.
Date:
In this reading seminar, I was asked to give talks on the basics of algebraic K-theory, the Serre-Swan theorem, the Grothendieck-Riemann-Roch theorem, Whitehead torsion and Reidemaster torsion. I divided these into three talks. In the first talk, I introduced the basics of $K_0$ (i.e. the definition and some examples of calculations, relative K-theory). In the second talk, we arrive at the Grothendieck-Riemann-Roch theorem with a geometric approach. The motivation is also discussed from a geometrical point of view. Finally, in the last lecture, I talked about Whitehead’s torsion and its application.