...ural isomorphism A ∼ −→ Σ2A. In particular for every point y ∈ Sing Y the subcategory ΓyS(R) is 2-periodic. As a corollary we obtain a geometric proof of a special case of a result due to Jesse Burke =-=[8]-=-. 12 GREG STEVENSON Corollary 6.2. Suppose A is an object of S(R). Then Hom(A,Σ2nA) ∼= 0 for some n ≥ 0 if and only if A ∼= 0. Proof. The if direction is clear. For the other direction let A be an obj...