Perverse equivalence in $SL(2,q)$

preprint2020arXivOpen access

We will be defining a type of perverse equivalence that always corresponds to a derived equivalence with two-term tilting complexes. We are going to show that the tilting considered by Okuyama and Yoshii for the proof of Broué's conjecture for $SL(2,q)$ in defining characteristic is a composition of such perverse equivalences.

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Perverse equivalence in $SL(2,q)$

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Perverse equivalence in SL(2,q)SL(2,q)SL(2,q)

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Perverse equivalence in $SL(2,q)$