4 problems

Integral Taylor expansion conjecture.

Let $f:Z\to X$ be a virtual Cartier divisor of derived Artin stacks, and let $\mathcal{F}\in\operatorname{Perf}(Z)$ be a perfect complex of rank $l$. Determinant conjecture. There…

Let $(f:X\rightarrow S)\in \mathcal{F}^n$ be a projective flat morphism of pure relative dimension $n$, and let $E$ be a vector bundle on $X$. Let $\lambda(E)$ denote the determina…

For each Riemann surface $S$, let $\operatorname{Loop}(S)$ be the space of loops in $S$, let $\operatorname{Det}\to\operatorname{Loop}(S)$ be the continuous positive determinant li…