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In 1998 Brou\'e, Malle and Rouquier conjectured that the Hecke algebra of afinite complex reflection group W is a free module over the algebra ofparameters of rank |W|. We give an exposition of a proof of this conjecture incharacteristic zero (and sufficiently large positive characteristic), due to I.Losev and I. Marin - G. Pfeiffer.

Proof of the Brou\'e-Malle-Rouquier conjecture in characteristic zero (after I. Losev and I. Marin - G. Pfeiffer)