10 problems

Let $n$ be an integer with $n\geq 3$, and let $R$ and $S$ be isomorphic filtered $\lambda$-ring structures on … Let $\sigma:R\xrightarrow{\cong}S$ be an isomorphism. A filtered…

Let $n$ be an integer with $n\geq 3$, and let … be a family of nonzero integers. A filtered $\lambda$-ring structure on $\mathbf{Z}[x]/(x^n)$ has prescribed Adams linear coefficien…

Let $n$ be an integer with $n\geq 3$. Consider the filtered truncated polynomial ring … A filtered $\lambda$-ring structure is a filtered $\lambda$-ring structure on this ring, and…

Let $S$ be a Noetherian scheme, let $G$ be a flat group scheme over $S$, and let $X$ be a $G$-scheme over $S$. A $G$-module on $X$ is an ${\mathcal O}_X$-module with the compatible…

Witt construction conjecture. The resulting object is canonically isomorphic to the full BC-system.

Let $X$ be a proper nonempty scheme, and let ${\mathfrak r}$ denote the product of all the real places. Real periodic-point conjecture. We conjecture that the real periodic locus ……

Let $A$ be an abelian variety of dimension $g$, let $K=K_0(A)\otimes\mathbf Q$, and let $\operatorname{Fil}^r_\Gamma$ be the gamma filtration associated with the composed lambda-ri…

Let $A$ be an abelian variety of dimension $g$ over an algebraically closed field of characteristic zero, and let $K_0(A)\otimes\mathbf Q$ carry its usual gamma filtration…

Let $\underline{\operatorname{K}}_0(\operatorname{Sch}^{ft})$ and $\underline{\operatorname{K}}^{\hat{\mu}}(\operatorname{Sch}^{ft})$ be the motivic ring theories over…

Virtual splitting principle. There should exist a larger $bb$-ring $R'$ containing $R$ such that $x$ is finite-dimensional in $R'$: there are line elements $ell_i,ell'_j$ in $R'$ w…