2 Search Results for "Narayanan, Ashvni"

Document
DOI: 10.4230/LIPIcs.ITP.2022.14
Formalizing the Ring of Adèles of a Global Field

Authors: María Inés de Frutos-Fernández

Published in: LIPIcs, Volume 237, 13th International Conference on Interactive Theorem Proving (ITP 2022)

Abstract
The ring of adèles of a global field and its group of units, the group of idèles, are fundamental objects in modern number theory. We discuss a formalization of their definitions in the Lean 3 theorem prover. As a prerequisite, we formalize 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 idèle class group.
Cite as

María Inés de Frutos-Fernández. Formalizing the Ring of Adèles of a Global Field. In 13th International Conference on Interactive Theorem Proving (ITP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 237, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{defrutosfernandez:LIPIcs.ITP.2022.14,
  author =	{de Frutos-Fern\'{a}ndez, Mar{\'\i}a In\'{e}s},
  title =	{{Formalizing the Ring of Ad\`{e}les of a Global Field}},
  booktitle =	{13th International Conference on Interactive Theorem Proving (ITP 2022)},
  pages =	{14:1--14:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-252-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{237},
  editor =	{Andronick, June and de Moura, Leonardo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2022.14},
  URN =		{urn:nbn:de:0030-drops-167232},
  doi =		{10.4230/LIPIcs.ITP.2022.14},
  annote =	{Keywords: formal math, algebraic number theory, class field theory, Lean, mathlib}
}
Document
DOI: 10.4230/LIPIcs.ITP.2021.5
A Formalization of Dedekind Domains and Class Groups of Global Fields

Authors: Anne Baanen, Sander R. Dahmen, Ashvni Narayanan, and Filippo A. E. Nuccio Mortarino Majno di Capriglio

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
Dedekind domains and their class groups are notions in commutative algebra that are essential in algebraic number theory. We formalized these structures and several fundamental properties, including number theoretic finiteness results for class groups, in the Lean prover as part of the mathlib mathematical library. This paper describes the formalization process, noting the idioms we found useful in our development and mathlib’s decentralized collaboration processes involved in this project.
Cite as

Anne Baanen, Sander R. Dahmen, Ashvni Narayanan, and Filippo A. E. Nuccio Mortarino Majno di Capriglio. A Formalization of Dedekind Domains and Class Groups of Global Fields. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{baanen_et_al:LIPIcs.ITP.2021.5,
  author =	{Baanen, Anne and Dahmen, Sander R. and Narayanan, Ashvni and Nuccio Mortarino Majno di Capriglio, Filippo A. E.},
  title =	{{A Formalization of Dedekind Domains and Class Groups of Global Fields}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{5:1--5:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.5},
  URN =		{urn:nbn:de:0030-drops-139004},
  doi =		{10.4230/LIPIcs.ITP.2021.5},
  annote =	{Keywords: formal math, algebraic number theory, commutative algebra, Lean, mathlib}
}
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