Proves the Pappas-Rapoport conjecture on canonical integral models of Hodge-type Shimura varieties with quasi-parahoric level at p, shows uniformization by integral local Shimura varieties, and proves the Kisin-Pappas conjecture on local model diagrams.
Meromorphic vector bundles on the Fargues--Fontaine curve
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We introduce and study the stack of \textit{meromorphic} $G$-bundles on the Fargues--Fontaine curve. This object defines a correspondence between the Kottwitz stack $\mathfrak{B}(G)$ and $\operatorname{Bun}_G$. We expect it to play a crucial role in comparing the schematic and analytic versions of the geometric local Langlands categories. Our first main result is the identification of the generic Newton strata of ${\operatorname{Bun}}_G^{\operatorname{mer}}$ with the Fargues--Scholze charts $\mathcal{M}$. Our second main result is a generalization of Fargues' theorem in families. We call this the \textit{meromorphic comparison theorem}. It plays a key role in proving that the analytification functor is fully faithful. Along the way, we give new proofs to what we call the \textit{topological and schematic comparison theorems}. These say that the topologies of $\operatorname{Bun}_G$ and $\mathfrak{B}(G)$ are reversed and that the two stacks take the same values when evaluated on schemes.
fields
math.NT 3years
2024 3verdicts
UNVERDICTED 3representative citing papers
Constructs functorial Igusa stacks for Hodge-type Shimura varieties, yielding a sheaf on Bun_G that controls cohomology and proves compatibility with the semisimple local Langlands correspondence of Fargues-Scholze while establishing torsion vanishing for proper cases.
Establishes a representability criterion for v-sheaf modifications of formal schemes and applies it to parahoric level structures on local shtukas, yielding local representability of integral models of local Shimura varieties under hyperspecial levels.
citing papers explorer
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On a conjecture of Pappas and Rapoport
Proves the Pappas-Rapoport conjecture on canonical integral models of Hodge-type Shimura varieties with quasi-parahoric level at p, shows uniformization by integral local Shimura varieties, and proves the Kisin-Pappas conjecture on local model diagrams.
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Igusa Stacks and the Cohomology of Shimura Varieties
Constructs functorial Igusa stacks for Hodge-type Shimura varieties, yielding a sheaf on Bun_G that controls cohomology and proves compatibility with the semisimple local Langlands correspondence of Fargues-Scholze while establishing torsion vanishing for proper cases.
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Relative representability and parahoric level structures
Establishes a representability criterion for v-sheaf modifications of formal schemes and applies it to parahoric level structures on local shtukas, yielding local representability of integral models of local Shimura varieties under hyperspecial levels.