Commutative Algebra Seminar
Hunter Simper
Purdue University
Ext and Local Cohomology of Thickenings of Ideals of Maximal Minors
Abstract: Let $R$ be the ring of polynomial functions in $mn$ variables with coefficents in $\mathbb{C}$, where $m>n$. Set $X$ to be the matrix in these variables and $I$ the ideal of maximal minors of this matrix. I will discuss the R-module structure of certain Ext and local cohomology modules arising from the rings $R/I^t$. In particular, for $i$ equal to the cohomological dimension of $I$, I will discuss the embedding of $Ext^i_R(R/I^t,R)$ into $H_\frak{m}^{mn}(R)$, explicitly describing this embedding when $X$ is size $n \times (n-1)$. More generally for $X$ of arbitrary size I will describe the annihilator of $Ext^i_R(R/I^t,R)$ and thereby completely determine the $R$-module structure of $H_\frak{m}^{mn-i}(R)$.
Tuesday September 6, 2022 at 11:00 AM in 636 SEO