Appears in collection : Algebraic Analysis in honor of Masaki Kashiwara's 70th birthday

If X is a smooth closed subscheme of an ambient smooth scheme Y, Calaque, Caldararu and Tu have endowed the shifted normal bundle NX/Y[−1] with a derived Lie algebroid structure. This structure generalizes the Lie algebra structure on the shifted tangent bundle TX[−1] on a smooth scheme, due to Kapranov and Markarian. In this talk, we will explain how a geometric condition on the pair (X,Y), originally discovered by Shilin Yu, allows to ensure that NX/Y[−1] is a true Lie object in the derived category D(X). Some geometric consequences of this result will be discussed. This is joint work with Damien Calaque.