Winter Term 2017/2018
Time and Place: Tuesday, 14:00-16:00 h, Arnimallee 7, SR 031
In this seminar we want to study algebraic K-theory. To every ring R (or more generally to every exact category, or Waldhausen category, or stable infinity-category) one associates a space (or spectrum), whose homotopy groups are denoted K_i(R). While K_0(R) and K_1(R) have very simple and concrete algebraic descriptions, higher algebraic K-theory groups are more involved and usually very difficult to compute.
Whereas the first talks in the seminar may only need basic knowledge in algebra, we will later also use concepts from algebraic topology and in particular homotopy theory.
The seminar language is English.
|17.10.|| Preliminary Discussion
||Holger Reich /
|07.11.||1. Wall’s finiteness obstruction||Tatiana Levinson|
|14.11.||2. K_0 of Dedekind domains||Alberto Richtsfeld|
|21.11.||3. K_2 and universal central extensions||Alexander Müller|
|28.11.||4. The K-theory space I||Georg Lehner|
|05.12.||5. The K-theory space II||Robert Cardona|
|12.12.||6. The additivity theorem I||Vincent Boelens|
|19.12.||7. The additivity theorem II||Vincent Boelens|
|09.01.||8. Quillen’s Q-construction||Anna Buhné|
|16.01.||9. Quillen’s plus construction|
|23.01.||10. Negative K-theory|
|30.01.||11. Assembly maps|
J. Milnor: Introduction to Algebraic K-Theory, Ann. of Mathematics Studies Number 72, 1971
I. Madsen and I. Patchkoria: Notes for Categories and Toplogy, Univ. Copenhagen, 2016