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Morgan Rogers (he/him) (Mar 01 2026 at 17:50):José M. R. Caballero said:
Consequently, in the ideal case scenario, by constructing an algebraic stack 𝒳_G associated with a network G, the characteristic polynomial of the network's adjacency matrix should be identified with the characteristic polynomial of the Frobenius operator acting on the first cohomology group H¹(𝒳_G, ℚ_ℓ) (or a related weighted sum across Hⁱ).
Where does the "should" in this sentence come from? What leads you to think that these things might be related?
Deleted user (Mar 01 2026 at 22:25):This is a guess based on the following coincidences:
Both represent "counting" functions (points on a variety vs. non-backtracking paths on a graph).
Both reduce to rational functions governed by characteristic polynomials.
David Michael Roberts (Mar 03 2026 at 08:09):In case it's not clear to anyone, the paragraph starting "In the framework of the Weil Conjectures" is almost surely (in the sense of measure theory) LLM-generated.