Explicit Conductors and Nearby Cycles for Strictly Semistable Varieties over Local Fields

Rahul Thakurdas Kundnani,Shri  Kant,Khursheed  Alam

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Explicit Conductors and Nearby Cycles for Strictly Semistable Varieties over Local Fields

R. T. Kundnani,

Sh. Kant,

K. Alam

2025-11-07

https://doi.org/10.24108/preprints-3113859

We develop a detailed framework for computing conductors and local cohomological invariants associated with strictly semistable varieties over non-archimedean local fields. By analyzing the interaction between vanishing cycles, nearby-cycle complexes, and higher ramification groups, we establish explicit expressions for the Swan part of the conductor and its variation under tame and wild extensions. The approach clarifies how local factors in the $\ell$-adic cohomology reflect the geometric structure of the special fiber and isolates the contributions arising from nontrivial monodromy actions. The resulting formulas yield a transparent description of the cohomological behavior within the semistable range and delineate the precise obstructions that occur beyond it. Applications include the decomposition of local zeta factors and the structural interpretation of wild ramification in arithmetic geometry over local fields.

Ссылка для цитирования:

Kundnani R. T., Kant Sh., Alam K. 2025. Explicit Conductors and Nearby Cycles for Strictly Semistable Varieties over Local Fields. PREPRINTS.RU. https://doi.org/10.24108/preprints-3113859

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