10 problems

Let $R$ be a Hecke symmetry of birank $(r,s)$, and let $C$ be the reflection operator introduced above. Assume that … It is known that $\operatorname{tr}(C)$ has the form $-[x]_q$…

Let $(A,\Gamma)$ and $(B,\Sigma)$ be flat Hopf algebroids, and let a weak equivalence mean a morphism of flat Hopf algebroids inducing an equivalence between their comodule categor…

Let $BP_{*}BP$-comodules be graded comodules over the Hopf algebroid $(BP_{*},BP_{*}BP)$. A hereditary torsion theory is a class of comodules closed under subobjects, quotients, ex…

Let $V$ be the defining comodule, and let $V_4$ and $\overline{V}_{\!\!4}$ be the $U_q(\mathfrak{spo}(2\,|\,2))$-submodules of $V\otimes V$ considered in the paper. Let…

Let $E_*$ be the coefficient ring of Morava $E$-theory at height $n$, let $E_*E$ be its cooperations, and let $v_0=p,v_1,\ldots,v_{n-1}$ denote the usual periodicity elements. For…

Assume $p$ is sufficiently large with respect to $n$. Let $E$ be the height-$n$ theory in the source, let $I_{n-1}$ be the corresponding invariant ideal, and let $L_{n-1}$ and…

Let $L_n$ be the algebraic localization functor at height $n$. An object $X$ is $E(n)_*$-local if, whenever $E(n)_*\otimes_{BP_*}T\simeq 0$, the space of maps…

Let $\operatorname{Stable}_{BP_*BP}$ be the stable category of $BP_*BP$-comodules. For each $n$, let $L_n^f$ denote finite localization with respect to a finite type $n$-spectrum,…

Let $\mathcal{A}_{ff}$ be the FRT algebra considered in the paper, and let a finite-dimensional comodule mean a finite-dimensional comodule over $\mathcal{A}_{ff}$. Power-of-two di…

Hovey–Strickland's conjecture. The Hopf algebroids $(A,\mathcal H)$ and $(B,\mathcal K)$ are connected by a chain of weak equivalences.