November 12, 2025Inventiones mathematicaeOpen Access

The connected components of affine Deligne–Lusztig varieties

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The computation identifies connected components across affine Deligne–Lusztig varieties and local Shimura varieties, indicating significant advancements in this area.
Key findings include the relationship to moduli spaces of p-adic shtukas, revealing substantial connections between these mathematical structures.
Analysis of these varieties employs v-sheaf-theoretic techniques and addresses folklore conjectures about their connectivity and geometrical properties.
These results may enable further investigations into the geometry of integral models of Shimura varieties and related groups, influencing future research directions.

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Implication

This analysis computes connected components in affine Deligne–Lusztig varieties, suggesting implications for moduli spaces and local Shimura varieties.

Cite This Study

Gleason et al. (2025) studied this question.

synapsesocial.com/papers/692523d4c0ce034ddc355597 https://doi.org/10.1007/s00222-025-01386-1

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Implication

This analysis computes connected components in affine Deligne–Lusztig varieties, suggesting implications for moduli spaces and local Shimura varieties.

The connected components of affine Deligne–Lusztig varieties

Key Points

Discussion

Implication

Cite This Study

The connected components of affine Deligne–Lusztig varieties

Key Points

Discussion

Implication

Cite This Study

Also Consider

Also Consider