A uniform construction of stacks BT^{G,μ}_n using stacky prismatic technology verifies Drinfeld's algebraicity conjecture and yields a linear-algebraic classification of truncated p-divisible groups over general p-adic bases.
On algebraic spaces with an action of G_m
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abstract
Let Z be an algebraic space of finite type over a field, equipped with an action of the multiplicative group $G_m$. In this situation we define and study a certain algebraic space equipped with an unramified morphism to $A^1\times Z\times Z$, where $A^1$ is the affine line. (If Z is affine and smooth this is just the closure of the graph of the action map $G_m\times Z\to Z$.) In articles joint with D.Gaitsgory we use this set-up to prove a new result in the geometric theory of automorphic forms and to give a new proof of a very important theorem of T. Braden.
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UNVERDICTED 2representative citing papers
Computes multiplicities of core Lagrangians in Hilbert schemes on elliptic surfaces and proposes mirror duality of very stable upward flows to modified Procesi bundles, supported by numerical checks and conjectures for wobbly cases.
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An algebraicity conjecture of Drinfeld and the moduli of $p$-divisible groups
A uniform construction of stacks BT^{G,μ}_n using stacky prismatic technology verifies Drinfeld's algebraicity conjecture and yields a linear-algebraic classification of truncated p-divisible groups over general p-adic bases.
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Equivariant multiplicities and mirror symmetry for Hilbert schemes
Computes multiplicities of core Lagrangians in Hilbert schemes on elliptic surfaces and proposes mirror duality of very stable upward flows to modified Procesi bundles, supported by numerical checks and conjectures for wobbly cases.