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19243901 Algebraic K-Theory

  • FU-Students should register via Campus Management and non-FU-students should register via MyCampus/Whiteboard.

Winter Term 2020/2021

Lecturer:  Dr. Gabriel Angelini-Knoll


  • Time and place:  Monday 10:00-12:00 h, online



Target group: The cours will be targeted at 3rd semester masters students.

Requirements: The prerequisites are Basismodul: Topology I-II and Aufbaumodul: Topologie III and Basismodul: Algebra I-II are recommended.


Content: Algebraic K-theory associates to a ring a graded abelian group. This invariant has a rich history and numerous applications. For example, the algebraic K-theory of group rings has applications to geometric topology, the algebraic K-theory of rings of integers in number fields has applications to number theory, and algebraic K-theory of the coordinate ring of an affine variety has applications to algebraic geometry. Following the insight of Quillen, Segal, and Waldhausen it is beneficial to generalize the input to a category and the output to a space whose homotopy groups are the algebraic K-theory groups. Therefore category theory and topology in addition to algebra are fundamental to the subject.

In this course, we will survey different constructions of algebraic K-theory, describe some fundamental properties of algebraic K-theory, and discuss some important applications.

Literature:

  • The K-book: an introduction to algebraic K-theory by Charles Weibel.