Self-equivalences of pseudo-projective planes II: simple equivalences

Reducibility of Self-homotopy Equivalences

We describe a new general method for the computation of the group Aut(X) of self-homotopy equivalences of a space. It is based on the decomposition of Aut(X) induced by a factorization of X into a product of simpler spaces. Normally, such decompositions require assumptions (’induced equivalence property’, ’diagonalizability’), which are strongly restrictive and hard to check. In this paper we d...

Equivalences in Bicategories

In this paper, we establish some connections between the concept of an equivalence of categories and that of an equivalence in a bicategory. Its main result builds upon the observation that two closely related concepts, which could both play the role of an equivalence in a bicategory, turn out not to coincide. Two counterexamples are provided for that goal, and detailed proofs are given. In par...

Equivalences of Derived Categories of Sheaves on Quasi-projective Schemes

We extend Orlov’s result on representability of equivalences to schemes projective over a field. We also investigate the quasi-projective case.

Self-equivalences of Stable Module Categories

Let P be an abelian p-group, E a cyclic p′-group acting freely on P and k an algebraically closed field of characteristic p > 0. In this work, we prove that every self-equivalence of the stable module category of k[P oE] comes from a self-equivalence of the derived category of k[P o E]. Work of Puig and Rickard allows us to deduce that if a block B with defect group P and inertial quotient E is...

Self-Homotopy Equivalences of Product Spaces