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arXiv · 2203.16344

Formalizing the Ring of Ad\`eles of a Global Field

María Inés de Frutos-Fernández
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Abstract

The ring of ad\`eles of a global field and its group of units, the group of id\`eles, are fundamental objects in modern number theory. We discuss a formalization of their definitions in the Lean 3 theorem prover. As a prerequisite, we formalized adic valuations on Dedekind domains. We present some applications, including the statement of the main theorem of global class field theory and a proof that the ideal class group of a number field is isomorphic to an explicit quotient of its id\`ele class group.

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María Inés de Frutos-Fernández. 2022-03-06. Formalizing the Ring of Ad\`eles of a Global Field. https://arxiv.org/abs/2203.16344

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