10 problems

Traverso's isogeny cutoff conjecture. The isogeny cutoff satisfies

Traverso's truncation conjecture. One has

Unconditional local Shimura conjecture. The natural transformation

Let $G$ be a smooth affine group scheme over ${\mathbb{Z}}/p^n{\mathbb{Z}}$ and let $\mu:{\mathbb{G}}_m\to G$ be 1-bounded. Let $\operatorname{BT}_n^{G,\mu,?}$ be the quotient 2-st…

Invariant-subvariety conjecture. The special fiber of $\mathfrak M_{\mathcal R,\Omega}$ contains a nonempty $Z(\mathbb A^{\infty,p})\times G(\mathbb A^{\infty,p}\otimes L^+)$-invar…

Let $Y$ be the object used to define the formally smooth deformation space $\mathbf{Def}_{\mathrm{sus}}(Y)$, and let $\mathfrak{a}_Y$ be its ambient Lie algebra. Let…

The arbitrary-Newton-polygon conjecture. For an arbitrary Newton polygon $\xi$, let $w\in{}^J W$ be a generic specialization of $w_\xi$. Then there exists a Newton polygon $\zeta$…

Versal-family pullback conjecture. Does there exist a variety $Y$ and a height-$2$, dimension-$1$ $p$-divisible group $\mathscr{H}$ on $Y$, everywhere versally deformed, together w…

Let $F$ be the relevant base field, let $O_D$ be the specified maximal order, and fix an $r$-special $p$-divisible group $({\mathbb {X}},\iota_{{\mathbb {X}}})$ over an algebraic c…

Let $k$ be a perfect field of characteristic $p$, let $W(k)$ be its ring of Witt vectors, let $K_0=W(k)[1/p]$, and let $K$ be a finite totally ramified extension of $K_0$ with ring…