Rosanna Laking "Tilts of the module category and cosilting pairs"

 The bounded derived category of a finite-dimensional algebra is well-known to encode useful homological information about its category of modules. In particular, the category modA of finite-dimensional A-modules appears a full subcategory of the derived category in such a way that the Ext-groups can be interpreted as homomorphisms in the derived category to shifted modules.  This is due to the fact that modA is the heart of a (faithful) t-structure (U, V) in the derived category.  In general, the derived category contains many other hearts of t-structures, which are abelian subcategories whose homological algebra is related to the homological algebra of A (to varying degrees).  

In this talk we will present recent joint work with Lidia Angeleri Hügel and Francesco Sentieri in which we focus on hearts of t-structures that are “nearby” (U,V): those that arise as tilts of (U,V).  We will discuss how the hearts relate to modA and how their presence can be detected in the category ModA of all A-modules.