4 problems

Avramov–Buchweitz–Iyengar's total rank conjecture. For every projective flag $D$, the inequality above should hold. The conjecture is false: Iyengar–Walker provided counterexamples…

Let $k$ be a field of characteristic zero, and let $\pi\colon S\twoheadrightarrow T$ be an epimorphism of local $k$-algebras essentially of finite type. An evolution of $T$ is such…

Let $X$ be an affine algebraic variety, and let the topological complex be the more general version of the complex considered in Vinogradov's work on invariants produced by derivat…

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…