Explicit Selmer Groups for Jacobians of Cyclic Prime Covers via Local Cohomology — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Explicit Selmer group computation for Jacobians of cyclic covers of P¹ of prime degree p, via local cohomology data, is the only substantive mathematical result in this set. | MATH: For isogeny φ: J→J on Jacobian J of cyclic p-cover of P¹, Sel^φ(J,k) ⊂ H¹(Gal(k̄/k), J[φ]) defined by local conditions; cyclic cover structure yields explicit local cohomology constraints. | CONNECTION: The cyclic p-cover of P¹ carries Galois group Z/p — a cyclic lattice symmetry. The Selmer group's local data implicitly involves roots of unity (p-th roots), linking to cyclotomic fields. No direct golden-ratio or base-60 constants appear. | DEPTH: 6 — This is a concrete, computable advance in arithmetic geometry (Selmer groups control Mordell-Weil rank via descent), but the provided abstract lacks explicit equations or constants; the depth is real but the extractable mathematical content is thin. --- **Detailed analysis of all five sources:** 1. **Perrot (cyclic cohomology, Lie groupoids)** — Th Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208822413
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