Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Applications of Homological Algebra Introduction to Perverse Sheaves Spring 2007 P. Achar
 

Summary: Applications of Homological Algebra Introduction to Perverse Sheaves
Spring 2007 P. Achar
Problem Set 10
March 29, 2007
1. A functor F : C1 C2 between two triangulated categories with t-structures is said to be t-exact if
F(C0
1 ) C0
2 and F(C0
1 ) C0
2 . Let DU , DZ, and D be categories of sheaves as in the theorem
on gluing of t-structures. Show that the t-structure on D described in that theorem is the unique
t-structure on D such that Ri : DZ D and j-1
: D DU are t-exact functors.
2. Suppose we give DU and DZ the standard t-structure. Show that the t-structure on D described by the
gluing theorem is the standard t-structure. Also, show that the middle-extension functor j! coincides
in this case with the (non-derived) extension-by-zero functor j!.
3. Suppose DU has the standard t-structure. By shifting the standard t-structure on DZ and then gluing,
can you obtain a t-structure on D for which the middle-extension functor coincides with the non-derived
push-forward j? How about Rj? Rj!? (Hint: The answers for j and Rj! are "yes." For Rj, it
depends on properties of the topological space U. You should find a condition on U under which the

  

Source: Achar, Pramod - Department of Mathematics, Louisiana State University

 

Collections: Mathematics