6 problems

Let $S=mathbbm{k}[x_1,\ldots,x_n]$ and $A=mathbbm{k}[t]$. Let $\operatorname{D^b_{DM}}(S)$ and $\operatorname{D^b_{DM}}(A)$ denote the relevant bounded derived categories of differe…

Let $S=mathbbm{k}[x_1,\ldots,x_n]$ and $A=mathbbm{k}[t]$. Let $mathbbm{B}$ be the vector space of Betti vectors, and let $\mathcal{E}$ be a vector bundle on $mathbbm{P}^{n-1}$ with…

Let $S=mathbbm{k}[x_1,\ldots,x_n]$ be a polynomial ring over a field $mathbbm{k}$. A degree sequence is the sequence of generating degrees of a pure resolution, and folding such a r…

Let $S=mathbbm{k}[x_1,\ldots,x_n]$ be a polynomial ring over a field $mathbbm{k}$. For an integer $a$, let $BS_{\text{mod}}(S)$ be the rational cone of Betti tables of graded finite…

Let $I$ be an open polysegment, let $P$ be a $\nabla$-module over $A^n_K(I)$ satisfying the Robba condition, and let $A$ be an exponent of $P$. A multisubset $B$ of…

Let $R$ be a regular local ring of dimension $d$, and let $F$ be a differential $R$-module admitting a finite free flag. If the homology $H(F)=\ker\delta/\operatorname{im}\delta$ h…