47 problems

Let $f_{\operatorname{Wt}}(z)=\sigma(z;g_2,g_3)$ be the Witten genus exponential, and recall that a formal power series $u+\sum_{n\geq 1}c_n\frac{u^{n+1}}{(n+1)!}$ with coefficient…

Universality conjecture. The formal group ${\frak F}(x\otimes 1,1\otimes x)$ is the universal object in the category of formal groups over a (topological) Hopf algebra.

Let $\mathcal{O}$ be the ring of integers of a finite extension of $\mathbb{Q}_p$. Let $f$ and $u$ be, respectively, a noninvertible series and a nontorsion invertible series defin…

Let $S$ be a K3 surface over a field of positive characteristic, and let $\hat{\operatorname{Br}}(S)$ denote its formal Brauer group. A K3 surface is supersingular when its formal…

General Ext-comparison conjecture. The displayed map is an isomorphism for all associative rings $R$, all $m\in\mathbb{Z}$, all $k\geq 0$, and all $R^{\operatorname{com}}$-modules…

Lubin's conjecture. Under these hypotheses,

Let $f:X\rightarrow\mathscr{A}_{g,\mathbb{F}}^{\mathrm{ord}}$ be a map from a smooth connected variety, let $x\in X(\mathbb{F})$, and let…

Cartier–Witt divisor conjecture. An $R$-point of $\widehat{\bbF}_1^\mathrm{Syn}$ is given by a formal group over $R$, a Cartier–Witt divisor on this pullback, and an isomorphism ov…

Let $\bbS^{\widehat{\mathbbl{\Delta}}}$ be the complement of the zero section in the universal formal group $\widehat{\bbG}_\mathrm{univ}=\bbS^{\widehat{\calN}}$, regarded as an an…

Let $\bbS^\mathrm{Syn}$ be the syntomic stack, and let $\bbM_{\mathrm{m}\ifthenelse{\equal{\bbS}{}}{}{,\bbS}}^\mathrm{Syn}$ be the associated monoid stack. Consider the map from…

Let $\bbS^\mathrm{Syn}$ be the syntomic stack and let $\bbM_{\mathrm{m}\ifthenelse{\equal{\bbS}{}}{}{,\bbS}}^\mathrm{Syn}$ be its associated monoid stack. Let…

Let $\bbS^{\widehat{\calN}}$ be the stack of one-dimensional commutative formal groups with a section, and let…

The paper considers a maximal finite subgroup $G'\subseteq \mathbb{G}_h$, a minimal-genus curve $X$ with automorphism group $G'$, the deformation stack $\operatorname{Def}_{(X,G)}$…

Let $C:\operatorname{Spec} R\to \mathcal{M}_{cub}$ be a cubic curve, and let $\widehat{C}$ denote its formal completion, a formal group over $R$. Write…

Let $(\mathrm{SpStk}^{\mathbf C\mathrm p})^{\mathrm B\mathbf T}$ denote the $\infty$-category of $\mathbf T$-equivariant complex periodic spectral stacks, and let…

Let $A$ be a finite abelian group, and let $\mathrm{MU}_A$ denote the equivariant complex cobordism spectrum. An equivariant formal group law is the equivariant analogue of a forma…

Let $\mathcal{B}$ be the Hopf algebra of formal diffeomorphisms of the non-commutative line, let $D(\mathcal{B})$ denote its Drinfeld quantum double, and let $M\xi$ be the Baker–Ri…

Let $\widehat{G}^\mathrm{Dr}$ be Drinfeld's formal group over the stack $\bbZ_p^{{\mathlarger{\mathbbl{\Delta}}}}$. Its pullbacks to the $q$-de Rham prism and along the Frobenius m…

Rezk's conjecture. The Coleman norm and Ando's algebraic criteria are closely related.

Let $K$ be a finite extension of $\mathbf{Q}_p$, with ring of integers $\mathcal{O}_K$ and maximal ideal $\mathfrak{m}_K$. Let $P,U\in T\cdot\mathcal{O}_K[[T]]$ satisfy … with…

Let $p$ be a prime, let $d\geq 1$, and write $X=(x_1,\ldots,x_d)$. Let $\operatorname{Preper}(u)$ denote the preperiodic points of $u$, and let $\Lambda(f)$ denote the zero set of…

Let $p$ be a prime, let $d\geq 1$, and write $X=(x_1,\ldots,x_d)$. For a power series $h\in\mathbb{Z}_p[[X]]^d$, let $\Lambda(h)$ denote its zero set. Commuting noninvertible forma…

Let $H_\Sigma$ be the formal group over the stack $\Sigma$ introduced above. An algebraization of $H_\Sigma$ is an isomorphism class of a smooth affine group scheme over $\Sigma$ w…

Formal-group isogeny conjecture. There exists a formal group $F$ with coefficients in $\mathcal{O}_K$, two endomorphisms $f_F$ and $u_F$ of $F$, and a nonzero power series $h$ such…

Let $\formalgroup$ be a formal group over a perfect field $k$. For a simplicial commutative $k$-algebra $A$, let $\theta(A)$ be its underlying $E_\infty$-algebra, and write…