Perverse equivalences and Brouéʼs conjecture

Alperin, 1976, Isomorphic blocks, J. Algebra, 43, 694, 10.1016/0021-8693(76)90135-6 Benson, 1998 Bonnafé, 2006, Coxeter orbits and modular representations, Nagoya Math. J., 183, 1, 10.1017/S0027763000009259 Bouc, 1999, Le complexe de chaînes dʼun G-complexe simplicial acyclique, J. Algebra, 220, 415, 10.1006/jabr.1999.7983 Broué, 1985, On Scott modules and p-permutation modules: an approach through the Brauer morphism, Proc. Amer. Math. Soc., 93, 401, 10.2307/2045600 Broué, 1990, Isométries parfaites, types de blocs, catégories dérivées, Astérisque, 181–182, 61 Broué, 1997, Sur certains éléments réguliers des groupes de Weyl et les variétés de Deligne–Lusztig associées, 73 Cabanes, 2004 Carlson, 2000, Self-equivalences of stable module categories, Math. Z., 233, 165, 10.1007/PL00004789 Chuang, 2007, Representations of Finite Groups and Tilting, 359 Chuang, 2008, Derived equivalences for the symmetric groups and sl2-categorification, Ann. of Math., 167, 245, 10.4007/annals.2008.167.245 J. Chuang, R. Rouquier, Calabi–Yau algebras and perverse equivalences, in preparation. Conway, 1985 Craven Dade, 1977, Remarks on isomorphic blocks, J. Algebra, 45, 254, 10.1016/0021-8693(77)90371-4 Deligne, 1973, Cohomologie à supports propres, vol. 305, 250 Digne, 2007, Cohomologie des variétés de Deligne–Lusztig, Adv. Math., 209, 749, 10.1016/j.aim.2006.06.001 Dudas, 2012, Coxeter orbits and Brauer trees, Adv. Math., 229, 3398, 10.1016/j.aim.2012.02.011 Dudas, 2013, Coxeter orbits and Brauer trees II, Int. Math. Res. Not. IMRN Dudas Erdmann, 1977, Principal blocks of groups with dihedral Sylow 2-subgroups, Comm. Algebra, 5, 665, 10.1080/00927877708822186 Fong, 1993, On perfect isometries and isotypies in finite groups, Invent. Math., 114, 139, 10.1007/BF01232665 Geck, 2006, Modular principal series representations, Int. Math. Res. Not., 2006, 1 Geck, 1997, Modular representations of finite groups of Lie type in non-defining characteristic, 195 H. Gollan, T. Okuyama, Derived equivalences for the smallest Janko group, preprint, 1997. Keller, 1998, On the construction of triangle equivalences, vol. 1685, 155 Koshitani, 2001, The principal 3-blocks of the 3-dimensional projective special unitary groups in non-defining characteristic, J. Reine Angew. Math., 539, 1, 10.1515/crll.2001.075 Koshitani, 2002, Brouéʼs conjecture holds for principal 3-blocks with elementary abelian defect group of order 9, J. Algebra, 248, 575, 10.1006/jabr.2001.9048 Koshitani, 2002, Brouéʼs conjecture for non-principal 3-blocks of finite groups, J. Pure Appl. Algebra, 173, 177, 10.1016/S0022-4049(01)00170-0 Koshitani, 2000, The principal 3-blocks of four- and five-dimensional projective special linear groups in non-defining characteristic, J. Algebra, 226, 788, 10.1006/jabr.1999.8167 Koshitani, 2001, Donovan conjecture and Loewy length for principal 3-blocks of finite groups with elementary abelian Sylow 3-subgroup of order 9, Comm. Algebra, 29, 4509, 10.1081/AGB-100106771 Kunugi, 2000, Morita equivalent 3-blocks of the 3-dimensional projective special linear groups, Proc. Lond. Math. Soc., 80, 575, 10.1112/S0024611500012387 Linckelmann, 1994, A derived equivalence for blocks with dihedral defect groups, J. Algebra, 164, 244, 10.1006/jabr.1994.1061 Linckelmann, 1996, Stable equivalences of Morita type for self-injective algebras and p-groups, Math. Z., 223, 87, 10.1007/BF02621590 Linckelmann, 1998, On derived equivalences and structure of blocks of finite groups, Turkish J. Math., 22, 93 Lusztig, 1976, Coxeter orbits and eigenspaces of Frobenius, Invent. Math., 38, 101, 10.1007/BF01408569 Marcus, 1996, On equivalences between blocks of group algebras: reduction to the simple components, J. Algebra, 184, 372, 10.1006/jabr.1996.0265 Marcus, 2002, Recent results on Brouéʼs abelian defect group conjecture Marcus, 2003, Tilting complexes for group graded algebras, J. Group Theory, 6, 175, 10.1515/jgth.2003.013 Marcus, 2005, Tilting complexes for group graded algebras. II, Osaka J. Math., 42, 453 T. Okuyama, Some examples of derived equivalent blocks of finite groups, preprint, 1997. T. Okuyama, Derived equivalences in SL2(q), preprint, 2000. Puig, 1990, Algèbres de source de certains blocs des groupes de Chevalley, Astérisque, 181–182, 221 Puig, 1999 J. Rickard, Derived equivalences for principal blocks of A4 and A5, preprint, 1990. Rickard, 1991, Derived equivalences as derived functors, J. Lond. Math. Soc., 43, 37, 10.1112/jlms/s2-43.1.37 Rickard, 1994, Finite group actions and étale cohomology, Publ. Math. Inst. Hautes Études Sci., 80, 81, 10.1007/BF02698896 Rickard, 1996, Splendid equivalences: derived categories and permutation modules, Proc. Lond. Math. Soc., 72, 331, 10.1112/plms/s3-72.2.331 Rouquier, 1995, From stable equivalences to Rickard equivalences for blocks with cyclic defect, vol. 212, 512 Rouquier, 1998, The derived category of blocks with cyclic defect groups, vol. 1685, 199 Rouquier, 2001, Block theory via stable and Rickard equivalences, 101 Rouquier, 2002, Complexes de chaînes étales et courbes de Deligne–Lusztig, J. Algebra, 57, 482, 10.1016/S0021-8693(02)00530-6 Rouquier, 2006, Derived equivalences and finite-dimensional algebras, 191 Rouquier, 2011, Automorphismes, graduations et catégories triangulées, J. Inst. Math. Jussieu, 10, 713, 10.1017/S1474748011000089 R. Rouquier, Local constructions in block theory, in preparation. Rouquier, 2003, Picard groups for derived categories, J. Lond. Math. Soc., 87, 197, 10.1112/S0024611503014059 Scott, 1990, Defect groups and the isomorphism problem, Astérisque, 181–182, 257 Yekutieli, 2004, The derived Picard group is a locally algebraic group, Algebr. Represent. Theory, 7, 53, 10.1023/B:ALGE.0000019383.78214.31