8 problems

Let $K$ be a complete discrete valued field with residue field of characteristic $p>0$, let $L/K$ be a finite Galois extension with Galois group $G$, and suppose that $k_L/k_K$ is…

Linear independence conjecture. The subset $\{\langle f_i\rangle\}_{i=1}^r$ of $X(A)$ is $\mathbb Z$-linearly independent.

Let $Q$ be the quotient of the Witt vector ring stack $W$ by its formal subgroup $\hat W$, let $T_F(Q)$ denote the associated Tate module, and let ${}^{s}W$ be the extension of $W$…

Achinger–Zdanowicz conjecture. There is a flat deformation of $X$ over the Witt vectors $W(k)$, not only over $W_2(k)$.

Let $A$ be a regular local ring with maximal ideal $\mathfrak{m}$, acted on by a finite group $G$, satisfying the assumptions of the Introduction, and let $k:=A/\mathfrak{m}$ be pe…

Let $\operatorname{Set}^{\mathrm{fin}}_{\cong}$ be the category of finite sets and bijections, let $\widetilde{K}(\operatorname{Set}^{\mathrm{fin}}_{\cong})$ denote its reduced alg…

Let $A$ be a ring, let $\operatorname{End}(A)$ be its category of endomorphisms, and let $V^{\geq j}\widetilde{K}(\operatorname{End}(A))$ be the induced Verschiebung filtration. Wr…

Let $A$ be the ring under consideration, and let $\widetilde{K}(\operatorname{End}(A))$ denote the reduced algebraic $K$-theory spectrum of its category of endomorphisms. Let…