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Improved Kunneth Tricks
Amnon Yekutieli
The Kunneth trick is a formula for the top cohomology of the derived tensor product of two complexes of modules over a ring. In this note we present two improvements of this formul…
Introduction to Derived Categories
Amnon Yekutieli
Derived categories were invented by Grothendieck and Verdier around 1960, not very long after the "old" homological algebra (of derived functors between abelian categories) was est…
The Squaring Operation for Commutative DG Rings
Amnon Yekutieli
Let A -> B be a homomorphism of commutative rings. The squaring operation is a functor Sq_{B/A} from the derived category D(B) of complexes B-modules into itself. The squaring oper…
Combinatorial Descent Data for Gerbes
Amnon Yekutieli
We consider descent data in cosimplicial crossed groupoids. This is a combinatorial abstraction of the descent data for gerbes in algebraic geometry. The main result is this: a wea…