05.11.2019 um 16:15 Uhr in 69/125:
Ilya Smirnov (Stockholm University)
Improving Lech's inequality
Lech's inequality is a fundamental inequality in a local ring that uniformly relates the multiplicity and the colength of a finite colength ideal. For monomial ideals there is a nice combinatorial proof and the general proof reduces to this case. Lech's inequality is never sharp in dimension at least two and in my talk I will present a way to fix it.
12.11.2019 um 16:15 Uhr in 69/125:
Yairon Cid Ruiz (MPI Leipzig)
Noetherian operators, primary submodules and symbolic powers
We give an algebraic and self-contained proof of the existence of the so-called Noetherian operators for primary submodules over general classes of Noetherian commutative rings. The existence of Noetherian operators accounts to provide an equivalent description of primary submodules in terms of differential operators. As a consequence, we introduce a new notion of differential powers which coincides with symbolic powers in many interesting non-smooth settings, and so it could serve as a generalization of the Zariski-Nagata Theorem.