Papers › Formalising the Local Compactness of the Adele Ring
Formalising the Local Compactness of the Adele Ring
Salvatore Mercuri
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The adele ring of a number field is a central object in modern number theory. Its status as a locally compact topological ring is one of the key reasons why. We describe a formal proof that the adele ring of a number field is locally compact implemented in the Lean 4 theorem prover. Our work includes the formalisations of new types, including the completion of a number field at an infinite place, the infinite adele ring and the finite S-adele ring, as well as formal proofs that completions of a number field are locally compact and that their rings of integers at finite places are compact.
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