6 problems

Let $X$ be a variety over $R$, let $Y$ be a closed subscheme of the special fiber $X_0$, and let $\mathcal{F}$ be an étale constructible sheaf of abelian groups on $X\times_R K$. W…

Let $\cV$ be a tensor $\lie{witt}_d$-module, with Lie derivative homomorphism … Let $\tau\colon \HH_2^{Lie}(\operatorname{End}\cV)\to\C$ be the functional determined by the univers…

Let $(A,d)$ be a connected, $q$-finite, and $q$-formal $\mathbb{k}$-CDGA. For $i\leq q$ and $s\geq 1$, let $\mathcal{R}^{i,s}(A)$ and $\mathcal{R}_{i,s}(A)$ denote the correspondin…

Invariance conjecture. The pullback functor

Let $\phi(p,q)=(pe^{pq},qe^{-pq})$ be the formal automorphism obtained from the equatorial Dehn twist, and let $\chi(x,y)=(x(1-xy),y(1-xy+(xy)^2+\ldots))$ be the formal automorphis…

A pipe is an object of the category of pipes, with realization denoted by $\underline{X}$. A pipe $X^c$ over $X$ is a pipe equipped with a map $X^c\to X$, and a pipe $Y^f$ under…