POINCARE ́ DUALITY IN HOCHSCHILD (CO)HOMOLOGY

These are notes on Van den Bergh’s analogue of Poincare ́ duality in Hochschild (co)homo-logy [16]. They are based on survey talks that I gave in 2006 in Göttingen, Cambridge and Warsaw and consist of an elementary explanation of the proof in terms of Ischebeck’s spec-tral sequence [10] and a detailed discussion of the commutative case, plus some motivating background material. The reader is assumed to be familiar with standard homological al-gebra, but the commutative algebra and algebraic geometry needed to understand the com-mutative case is recalled. For more preliminaries see e.g. [5, 15] (commutative algebra and algebraic geometry), [13] (noncommutative rings) and [1, 3, 18] (homological algebra)