Functorial approach to rank functions
 
 
Description: 

Motivated by the work of Cohn and Schofield on Sylvester rank functions on rings, Chuang and Lazarev have recently introduced the notion of a rank function on a triangulated category. A rank function is a nonnegative real-valued, additive, translation-invariant function on the objects of a triangulated category for which the triangle inequality on distinguished triangles holds. It turns out that a rank function on a triangulated category C can be recast as translation-invariant additive function on its abelianisation mod-C. This allows us to relate integral-valued rank functions on C with endofinite cohomological functors on C and, when C is the subcategory of compact objects of a compactly generated triangulated category T, with endofinite objects in T and certain closed sets of the Ziegler spectrum of T.

This talk is based on joint work with Mikhail Gorsky, Frederik Marks and Alexandra Zvonareva.

Date:  2022-03-30
Start Time:   15:00
Speaker:  Teresa Conde (Univ. of Stuttgart, Germany)
Institution:  University of Stuttgart, Germany
Place:  Remote seminar via Zoom: https://videoconf-colibri.zoom.us/j/81787306524
Research Groups: -Algebra and Combinatorics
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