Conditional Degree-One Boundary Decompositions for Hodge-Type Shimura Varieties at Hyperspecial Level

Rahul Thakurdas Kundnani,Shri  Kant,Khursheed  Alam,Vinoth  Marimuthu

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Conditional Degree-One Boundary Decompositions for Hodge-Type Shimura Varieties at Hyperspecial Level

R. T. Kundnani,

Sh. Kant,

K. Alam,

V. Marimuthu

2026-05-03

https://doi.org/10.24108/preprints-3113856

We study the low-degree Leray spectral sequence attached to the open immersion of an integral canonical model of a Hodge-type Shimura variety into a toroidal compactification. Under an explicit package of auxiliary assumptions on boundary regularity, cohomological purity, constructibility of the degree-one boundary sheaf, and vanishing of the degree-one Leray transgression, we obtain a low-degree edge-surjectivity statement and a Hecke-equivariant short exact sequence in degree one. We then formulate a conditional boundary criterion, expressed in terms of rational boundary tori, for the vanishing of the degree-one boundary contribution, assuming a compatible description of the boundary module. The resulting consequences are formal and conditional, and examples are included to illustrate both anisotropic and non-anisotropic situations.

Ссылка для цитирования:

Kundnani R. T., Kant Sh., Alam K., Marimuthu V. 2026. Conditional Degree-One Boundary Decompositions for Hodge-Type Shimura Varieties at Hyperspecial Level. PREPRINTS.RU. https://doi.org/10.24108/preprints-3113856

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