engleski

Equivariant sheaves and torsors beyond groupoids

In my earlier work in noncommutative geometry I introduced analogues of torsors for coactions of Hopf algebras on nonaffine noncommutative spaces. A puzzling class of 'big' examples called for nonflat descent, which should be replaced for geometric purposes by (derived) descent -- up to higher homotopies. Combinatorially, similar higher cocycles appear also in the study of descent for weak actions of categorical groups (in ordinary "commutative" geometry) and bigroupoids. These objects are relevant for study of "differential geometry of gerbes" now popular in geometry and physics. The notion of equivariant sheaf in this setup is far more involved than in 1-categorical situation. I will outline our work in progress concerning these ideas.

equivariant sheaf; groupoid; Hopf algebra; 2-categories; fibered categories

Abstract je objavljen u zborniku abstracta (proljece 2005) i tema prihvacena za izlaganje, no samo predavanje/putovanje nije odrzano zbog bolesti predavaca. Prilozi za zbornik radova tek slijede.