  Let R be a commutative noetherian ring. We prove that if R is either an
equidimensional finitely generated algebra over a perfect field, or an
equidimensional equicharacteristic complete local ring with a perfect residue
field, then the annihilator of the singularity category of R coincides with the
Jacobian ideal of R up to radical. We establish a relation between the
annihilator of the singularity category of R and the cohomological annihilator
of R under some mild assumptions. Finally, we give an upper bound for the
dimension of the singularity category of an equicharacteristic excellent local
ring with isolated singularity. This extends a result of Dao and Takahashi to
non Cohen-Macaulay rings.
