The spectrum of the inertia operator on the motivic Hall algebra

10 November 2015
Kai Behrend

Following an idea of Bridgeland, we study the operator on the K-group of algebraic stacks, which takes a stack to its inertia stack.  We prove that the inertia operator is diagonalizable when restricted to nice enough stacks, including those with algebra stabilizers.  We use these results to prove a structure theorem for the motivic Hall algebra of a projective variety, and give a more conceptual definition of virtually indecomposable stack function.  This is joint work with Pooya Ronagh.

  • Algebraic and Symplectic Geometry Seminar