Course description:
Tensor triangular geometry (tt-geometry) provides a framework for studying tensor triangulated categories through geometric methods, analogous to the way algebraic geometry allows us to study commutative rings geometrically. This course is an introduction to tt-geometry as well as an invitation to some of the more advanced topics in the subject.
We begin with an introduction to the foundational concepts of tt-geometry, with a particular emphasis on the lattice-theoretic approach, and explore some of the standard techniques to compute the tt-spectrum. In the second part of the course, we examine variants of the tt-spectrum, such as the homological spectrum, as well as the resulting support theories, and develop the theory of stratification for `big' tt-categories. Throughout, a wide range of examples will be discussed to illustrate the abstract theory and clarify the main results. The final part of the course will touch upon more recent developments in the field. Among other things, this might include applications to representation theory and equivariant homotopy theory, taking into account the interests of the participants.
Prerequisites: Familiarity with basic category theory and homological algebra is assumed. Prior exposure to triangulated categories or higher category theory may be helpful.
Time, Date and Location: Thursday 11.15-13, MPIM Seminar Room.
This course will be taught together with Tobias Barthel.
Lecture 1: Intro + Stone duality, notes
Lecture 2: Stone duality + Basic tt-geometry, notes
Lecture 3: Comparison map and Nilpotence theorem, notes