表現論セミナー Cohomology of local torsion free functors on intersection lattices（Paul Muecksch）

開催日時

2023年3月10日 15時00分 ～ 2023年3月10日 16時30分

場所

理学部3-413

講演者

Paul Muecksch氏 (Kyushu University)

We study a certain class of functors from the intersection
lattice of a hyperplane arrangement to the category of finitely
generated modules over the coordinate ring of the ambient space.
Important examples of local torsion free functors are derived from
modules of logarithmic vector fields. Such functors can also be regarded
as sheaves on finite spaces. We will demonstrate that their cohomology
controls the projective dimension of the associated module of global
sections. As an application, new exact sequences due to Takuro Abe can
be used to obtain exact sequences of functors associated to deleted and
restricted arrangements.