Cohomological Invariants of Frobenius Splittings and the Spectral Decomposition of the Cartier Algebra on Post-Singularity Varieties
Year: 2025
Type: article
Abstract: Mathematical Applications of Science Fiction We construct a rigorous cohomological framework for analyzing the spectral properties of the Cartier algebra on a class of schemes designated as Post-Singularity Varieties. By extending the classical theory of Frobenius splittings to the derived category of coherent sheaves, we define the Void-Walker Filtration on local cohomology modules. We prove that for a Post-Singularity Variety admitting a compatible Frobenius splitting, the spectral sequence associated with the Cartier operator degenerates at the second page, yielding a canonical decomposition of the intersection cohomology. Furthermore, we establish the existence of the Theron Invariant, a numerical quantity derived from the fractal dimension of the F-signature, which governs the topological stability of the variety under void-field perturbations. This work provides the algebraic foundation for understanding the quantization of geometric singularities in high-energy void dynamics.
Authors: Revista, Zen, MFC, 10
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7117665262
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