Speaker: Sergey Galkin
Title: Phantom categories
Date: Nov 8, 2012, 10:30 - 12:15
Place: RIMS, Room 006
Abstract:
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.