Algebra & Number Theory Seminar | Department Home

Texas Tech University
Algebra & Number Theory Seminar

Department of Mathematics & Statistics
Math 110
Wednesdays 3:00-4:00 pm

Sergio Estrada

University of Murcia

Wednesday, 21 March, 2018

Math 110, 3:00 pm

Title: On the right notion of the homotopy category of projectives over a non affine scheme

Abstract: The category of quasi-coherent sheaves on a non-affine scheme is well known not to have enough projectives. Neeman and Murfet have remedied this lack by defining the derived category of flats as a suitable replacement of the homotopy category of projectives. This is so because a celebrated result by Neeman states that, in the affine case, the two categories are equivalent. But many concrete schemes satisfy the so-called resolution property, i.e. they have enough locally frees (so, in particular, enough infinite dimensional vector bundles in the sense of Drinfeld) which constitute a better replacement of the flats. In the talk we will show that, for such schemes, the derived category of flats is still triangulated equivalent to the derived category of vector bundles. The equivalence is indirect and strongly uses the class of very flat sheaves as recently defined by Positselski.