Speaker: Vivek Mukundan
Affiliation: IIT Delhi
Title: Berger conjecture, valuations and torsions
Date and Time: December 12, 2022, 16:00:00 Hours
Venue: AG-77
Asbtract: Let $(R,\mathfrak{m}_R,\mathbb m{k})$ be a one-dimensional complete local reduced $\mathbb m{k}$-algebra over a field of characteristic zero. Berger conjectured that $R$ is regular if and only if the universally finite module of differentials $\Omega_R$ is torsion free. We discuss methods that have been used in the past to prove cases where the conjecture holds. When $R$ is a domain, we prove the conjecture in several cases. Our techniques are primarily reliant on making use of the valuation semi-group of $R$. First, we establish a method of verifying the conjecture by analyzing the valuation semi-group of $R$ and orders of units of the integral closure of $R$. We also prove the conjecture in the case when certain monomials are missing from the monomial support of the defining ideal of $R$. This also generalizes previous known results. This is joint work with Craig Huneke and Sarasij Maitra.
Affiliation: IIT Delhi
Title: Berger conjecture, valuations and torsions
Date and Time: December 12, 2022, 16:00:00 Hours
Venue: AG-77
Asbtract: Let $(R,\mathfrak{m}_R,\mathbb m{k})$ be a one-dimensional complete local reduced $\mathbb m{k}$-algebra over a field of characteristic zero. Berger conjectured that $R$ is regular if and only if the universally finite module of differentials $\Omega_R$ is torsion free. We discuss methods that have been used in the past to prove cases where the conjecture holds. When $R$ is a domain, we prove the conjecture in several cases. Our techniques are primarily reliant on making use of the valuation semi-group of $R$. First, we establish a method of verifying the conjecture by analyzing the valuation semi-group of $R$ and orders of units of the integral closure of $R$. We also prove the conjecture in the case when certain monomials are missing from the monomial support of the defining ideal of $R$. This also generalizes previous known results. This is joint work with Craig Huneke and Sarasij Maitra.