FormalConjectures.Wikipedia.KummerVandiver

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import FormalConjecturesUtil

Kummer–Vandiver conjecture

Reference: Wikipedia


open NumberField CyclotomicField IsCyclotomicExtension


namespace KummerVandiver

Kummer–Vandiver conjecture states that for every prime $p$, the class number of the maximal real subfield of $\mathbb{Q}(\zeta_p)$ is not divisible by $p$.

@[category research open, AMS 11]
theorem declaration uses 'sorry'kummer_vandiver (p : ℕ+) (hp : p.Prime) :
    ¬ ↑p ∣ (classNumber (maximalRealSubfield (CyclotomicField p ℚ))) := byp:ℕ+hp:p.Prime⊢ ¬↑p ∣ classNumber ↥(maximalRealSubfield (CyclotomicField ↑p ℚ))
  sorryAll goals completed! 🐙


end KummerVandiver