Systematic framework for encoding Galois representations ρ: Gal (ℚ̄/ℚ) → GLₙ (K) into spectral operators H_ρ. Key innovations: Frobenius-Spectral Correspondence (Frobenius eigenvalues → operator eigenvalues), Ramification Encoding via singular potentials at bad primes, ℓ-adic structure preservation through fractal scaling. The most fundamental tool in the arithmetic spectral toolkit — Galois representations underlie modular forms (Langlands) and arithmetic geometry (étale cohomology). Applications to Artin conjecture, Serre's modularity, potential automorphy.
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Thierry Marechal
F5 Networks (United States)
F5 Networks (United States)
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Thierry Marechal (Wed,) studied this question.
synapsesocial.com/papers/69c6206115a0a509bde18e31 — DOI: https://doi.org/10.5281/zenodo.19221706
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