| Sunday 29 June 2025 | |
| Events for day: Thursday 19 October 2023 |
| 14:30 - 16:30 Commutative Algebra Webinar Homotopy Lie Algebra of Tor-independent Tensor Products School MATHEMATICS Given surjective maps $varphi_1:R o S_1$ and $varphi_2:R o S_2$ of local rings with $mathrm{Tor}^R_{i>0}(S_1,S_2)=0$, in this talk we focus on the structure of the homotopy lie algebra $pi(S)$ of $S:=S_1otimes_RS_2$. We will see in various cases this is isomorphic to the pullback of Lie algebras $pi(S_1) times_{pi(R)} pi(S_2)$. As an application, the Poincare series of the residue field of $S$ can be written in terms of the ones of $S_1$, $S_2$, and $R$. Also, I will address some common properties that local homomorphism $varphi_1$ and $varphi_2$ share with $varphi: R o S$. The key ingredients are minimal models described in chapter 7 of A ... |