Source-pinned research
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Clear filtersIsDedekindDomain.HeightOneSpectrum.exists_adicValued_mul_sub_le
Plain-language statement
Given a, b β A and v b β€ v a we can find y in A such that y is close to a / b by the valuation v.
Source project: Fermat's Last Theorem
Person-level attribution pending.
IsDedekindDomain.HeightOneSpectrum.exists_adicValued_sub_lt_of_adicCompletionInteger
Plain-language statement
An element of πͺ_v can be approximated by an element of A.
Source project: Fermat's Last Theorem
Person-level attribution pending.
IsDedekindDomain.HeightOneSpectrum.exists_forall_adicValued_sub_lt
Plain-language statement
An element of β_{v β s} πͺ_v, with s finite, can be approximated by an element of A.
Source project: Fermat's Last Theorem
Person-level attribution pending.
IsDedekindDomain.HeightOneSpectrum.Extension.finite
Plain-language statement
There are only finitely many nonzero primes of B above a nonzero prime of A.
Source project: Fermat's Last Theorem
Person-level attribution pending.
IsDedekindDomain.HeightOneSpectrum.Extension.tensorAdicCompletionIntegersToAdicCompletion_range_eq_integers
Plain-language statement
The range of adicCompletionIntegers.tensorToAdicCompletion is π_w.
Source project: Fermat's Last Theorem
Person-level attribution pending.
IsDedekindDomain.HeightOneSpectrum.Extension.valued_adicCompletionSemialgHom
Plain-language statement
The local ramification index for the extension L_w/K_v is equal to the global ramification index for the extension w/v. In other words, if x in K_v and i:K_v->L_w then w(i(x))=v(x)^e where e is computed globally.
Source project: Fermat's Last Theorem
Person-level attribution pending.