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Grantor: Czech Academy of Sciences

**Objectives**:

The derived category of an abelian category is a meeting point between algebra and homotopical methods originally designed for topology. This project aims to extend the current knowledge about derived categories in the following directions. 1) Extend the recent description of equivalence classes of (big) tilting modules over an arbitrary commutative ring to the setting of silting complexes, or even compactly generated t-structures. 2) Describe the cotilting modules, or even the cosilting modules, over arbitrary Pruefer domain. Study the derived equivalences these modules induce. 3) Search for a purely tensor triangulated category construction of a non-compactly generated smashing localization based on an algebraic construction by Bazzoni and Šťovíček used for the module category of a valuation domain. The possible application could help solve the long open Telescope Conjecture for the homotopy category of spectra. The three topics are are strongly connected to each other and are expected to be studied simultaneously.

Main investigator:

Participating institutions:

Institute of Mathematics, AS CR