Formalising the local compactness of the adele ring
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916844140494848 |
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| author | Mercuri, Salvatore |
| author_facet | Mercuri, Salvatore |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19270 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Formalising the local compactness of the adele ring Mercuri, Salvatore Logic in Computer Science Number Theory 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. |
| title | Formalising the local compactness of the adele ring |
| topic | Logic in Computer Science Number Theory |
| url | https://arxiv.org/abs/2405.19270 |