Speaker: Sergey Galkin
Title: Phantom categories
Date: Nov 8, 2012, 10:30 - 12:15
Place: RIMS, Room 006
It was expected that Hochschild homology and Grothendieck K-group are conservative invariants for geometric categories (admissible subcategories in the bounded derived categories of coherent sheaves), that is vanishing of these invariants was supposed to imply vanishing of the respective category itself. Last half-year saw a burst of counter-examples, so-called (quasi-)phantom categories, related to various surfaces of general type with vanishing geometric genus (Godeaux 1206.1830, Burniat 1208.4348, Beauville 1210.3339, Barlow 1210.0343) and their products (1209.6183). I'll tell about these constructions and some remaining weird open questions.