Geodesic
Algèbre, Géométrie algébrique
Topological proofs of results on large fields
Walsberg, Erik1 
1 Department of Mathematics, University of California, Irvine, USA
Comptes Rendus. Mathématique, Tome 360 (2022) no. G11, pp. 1187-1192.

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We use the recently introduced étale open topology to prove several known facts on large fields. We show that these facts lift to a quite general topological setting.

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DOI : 10.5802/crmath.305

Walsberg, Erik 1

1 Department of Mathematics, University of California, Irvine, USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Topological proofs of results on large fields},
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Walsberg, Erik. Topological proofs of results on large fields. Comptes Rendus. Mathématique, Tome 360 (2022) no. G11, pp. 1187-1192. doi : 10.5802/crmath.305. https://geodesic-test.mathdoc.fr/articles/10.5802/crmath.305/

[1] Bachmayr, Annette; Harbater, David; Hartmann, Julia; Pop, Florian Large fields in differential Galois theory, J. Inst. Math. Jussieu, Volume 20 (2021) no. 6, pp. 1931-1946 | Zbl | MR | DOI

[2] Bary-Soroker, Lior; Fehm, Arno Open problems in the theory of ample fields, Geometric and differential Galois theory (Séminaires et Congrès), Volume 27, Société Mathématique de France, 2013, pp. 1-11 | MR

[3] Fehm, Arno Subfields of ample fields. Rational maps and definability, J. Algebra, Volume 323 (2010) no. 6, pp. 1738-1744 | MR | Zbl | DOI

[4] Fehm, Arno Embeddings of function fields into ample fields, Manuscr. Math., Volume 134 (2011) no. 3-4, pp. 533-544 | Zbl | MR | DOI

[5] Harbater, David On function fields with free absolute Galois groups, J. Reine Angew. Math., Volume 632 (2009), pp. 85-103 | Zbl | MR | DOI

[6] Harbater, David; Stevenson, Katherine F. Local Galois theory in dimension two, Adv. Math., Volume 198 (2005) no. 2, pp. 623-653 | Zbl | MR | DOI

[7] Johnson, Will; Tran, Minh; Walsberg, Erik; Ye, Jinhe Étale open topology and the stable field conjecture (2021) (https://arxiv.org/abs/2009.02319)

[8] Pop, Florian Embedding problems over large fields, Ann. Math., Volume 144 (1996) no. 1, pp. 1-34 | Zbl | MR | DOI

[9] Pop, Florian Little survey on large fields - old & new, Valuation Theory in Interaction. Proceedings of the 2nd international conference and workshop on valuation theory (EMS Series of Congress Reports), European Mathematical Society, 2014, pp. 432-463 | Zbl | DOI

[10] Srinivasan, Padmavathi A virtually ample field that is not ample, Isr. J. Math., Volume 234 (2019) no. 2, pp. 769-776 | MR | Zbl | DOI

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