fr:recherche [Guillaume ROND]

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====== Publications ======

<del>{{:fr:bishop-surfaces-non-algebraically-equivalent final.pdf | Real algebraic surfaces biholomorphically equivalent but not algebraically equivalent}}</del> preprint, 9pp. There is a mistake in the proof of Lemma 5. This affects the proof the main result, and we do not know whether it is true.

{{:fr:ploskiapprthm.pdf | Ploski Approximation Theorem}} (with Adam Parusiński), preprint, 12pp.

{{:fr:eisenstein-theorem.pdf | About Eisenstein's Theorem}} preprint, 14pp.

{{:fr:nashpoints_1.pdf | On the Nash points of subanalytic sets}} (with André Belotto da Silva and Octave Curmi), J. Singul. 27, 68-88, (2024). 

{{:fr:gabrielov_na_2.pdf | On rank Theorems for morphisms of local rings}} (with André Belotto da Silva and Octave Curmi), preprint, 35 pp.

{{:fr:preordresv_groupes_jan22.pdf | Preordered groups  and valued fields}} (with Julie Decaup), preprint, 38 pp.

{{:fr:CR_Mir_Lamel.pdf | Unique jet determination of CR maps into Nash sets}} (with Nordine Mir and Bernhard Lamel), Adv. Math, 432, 109271, (2023).

{{:fr:Aroca2022_Article_TheMinimalConeOfAnAlgebraicLau.pdf | The minimal cone of an algebraic Laurent series}} (with Fuensanta Aroca and Julie Decaup), Math. Annalen, 382, No. 3-4, (2022), 1745-1773. 

{{ https://jep.centre-mersenne.org/item/10.5802/jep.173.pdf| A proof of Gabrielov's rank Theorem}} (with André Belotto da Silva and Octave Curmi), J. Éc. polytech. Math., 8, (2021), 1329-1396.

{{:fr:algebraic_power_series_rev.pdf | Finiteness results concerning algebraic power series}} (with Fuensanta Aroca and Julie Decaup), J. Pure Appl. Algebra, 225, (2021), no. 6.

{{:fr:artin_approximation_over_banach_spaces.pdf |Artin approximation over Banach spaces}}, Commun. Algebra, 48, No. 10, (2020), 4214-4223.

{{:fr:CMH-2020-095-002-05.pdf |Algebraic varieties are homeomorphic to varieties defined over number fields}} (with Adam Parusiński), Comment. Math. Helv., 95, No. 2, (2020), 339-359.

{{:fr:tran8061.pdf |Multiparameter perturbation theory of matrices and linear operators}} (with Adam Parusiński), Trans. Amer. Math. Soc., 373, 4, (2020), 2933-2948. 

{{ https://arxiv.org/pdf/1905.06222.pdf |Transcendental holomorphic maps between real algebraic manifolds in a complex space}}, Proceedings of the A.M.S., 148, 5, (2020), 2097-2102. 

{{:fr:aroca_et_al-2018-proceedings_of_the_london_mathematical_society.pdf| Support of Laurent series algebraic over the field of formal power series}} (with Fuensanta Aroca), Proc. London Math. Soc., 118, 3 (2019), 577-605.

{{ :fr:1563242417.pdf |Remarks on Artin approximation with constraints}} (with Dorin Popescu), Osaka J. Math., 56, 3, (2019), 431-440.

{{:fr:10.1007_s00229-018-1025-0.pdf |Linear nested Artin approximation Theorem for algebraic power series}} (with Francisco-Jesús Castro-Jiménez and Dorin Popescu), Manuscr. Math., 158, 1-2, (2019), 55-73. 

{{:fr:ant-v12-n5-p06-p.pdf |Local topological algebraicity with algebraic coefficients of analytic sets or functions}}, Algebra Number Theory, 12 (2018), no 5, 1215-1231. 

{{ https://arxiv.org/pdf/1506.04717.pdf| Artin Approximation}}, J. Singul., 17 (2018), 108-192. 

{{ :fr:algebraicity_criterion2.pdf| Local zero estimates and effective division in rings of algebraic power series}}, J. Reine Angew. Math., 737 (2018), 111-160.

{{ https://arxiv.org/pdf/1602.06933.pdf | Higher order approximation of analytic sets by topologically equivalent algebraic sets }} (with Marcin Bilski, Krzysztof Kurdyka and Adam Parusiński), Math. Z., 288 (2018), no. 3-4, 1361-1375. 

{{ https://arxiv.org/pdf/1605.05577.pdf | An irreducibility criterion for power series }} (with Bernd Schober), Proceedings of the A.M.S., 145 (2017), no 11, 4731-4739. 

{{ :fr:jag667-1.pdf | Local topological algebraicity of analytic function germs}} (with Marcin Bilski and Adam Parusiński), J. Algebraic Geom., vol. 26, (2017), 177-197. 

{{ https://www.journalofsing.org/volume16/rond.pdf| About the algebraic closure of the field of power series in several variables in characteristic zero}}, J. Singul., 16, (2017), 1-51. 

{{:fr:struct_newlms.pdf | The analogue of Izumi's Theorem for Abhyankar valuations}} (with Mark Spivakovsky), J. Lond. Math. Soc.,  vol. 90 (3), (2014),  725-740. 

{{ https://arxiv.org/pdf/1301.2419.pdf| Łojasiewicz inequality over the ring of power series in two variables}}, Math. Res. Lett., vol. 20 (2), (2013), 1-13. 

{{ https://arxiv.org/pdf/1103.2559.pdf| The Abhyankar-Jung Theorem}}, (with Adam Parusiński), Journal of Algebra, vol. 365, (2012), 29-41. 

{{ :fr:approxi_reel.pdf | Approximation of holomorphic solutions of a system of real analytic equations}}, (with Michel Hickel), Canad. Math. Bull, vol. 55 (4), (2012), 752–761. 

{{ https://arxiv.org/pdf/1301.2418.pdf| Bornes effectives des fonctions d'approximation des solutions formelles d'équations binomiales}}, Journal of Algebra, vol. 323, no. 9, (2010), 2547-2555. 

{{ :fr:cras-popescu.pdf | Sur la lissification de type Płoski-Popescu}}, C. R. Math. Acad. Sci. Paris, vol. 348, no. 13-14, (2010), 727-729. 

{{ https://arxiv.org/pdf/1301.1154.pdf | Asymptotic behaviour of standard basis}}, Proceedings of the A.M.S., vol. 138 (2010), 1979-1982. 

{{ https://arxiv.org/pdf/math/0612214.pdf | Homomorphisms of local algebras in positive characteristic}}, Journal of Algebra, vol. 322, no. 12, (2009), 4382-4407. 

{{ :fr:series_de_poincare_smf.pdf | Séries de Poincaré motiviques des singularités d'hypersurfaces irréductibles quasi-ordinaires}}, Diff. eq. & Sing., 60th year of J. M. Aroca, Astérisque, 323, (2009), 371-396. 

{{ :fr:tordesillas.pdf |Propriétés de régularité des morphismes d'algèbres analytiques}}, Rev. Semin. Iberoam. Mat., vol. 3 fasc. V-VI (2008), 125-145. 

{{ :fr:artin-gabrielov2.pdf | Approximation de Artin cylindrique et morphismes d'algèbres analytiques}}, Proceedings of the Lêfest, Contemp. Math., vol. 474, (2008), 299-307. 

{{ :fr:sapporo.pdf | Exemples de fonctions de Artin de germes d'espaces analytiques}}, Adv. Stud. Pure Math., vol. 46, (2007), 197-210. 

{{ https://arxiv.org/pdf/math/0505679.pdf| Approximation diophantienne dans les corps de séries en plusieurs variables}}, Ann. Institut Fourier, vol. 56, no. 2, (2006), 299-308.  

{{ https://arxiv.org/pdf/math/0502045.pdf| Lemme d'Artin-Rees, théorème d'Izumi et fonction de Artin}}, Journal of Algebra, vol. 299, no. 1, (2006), 245-275.  

{{ https://arxiv.org/pdf/math/0412284.pdf| Sur la linéarité de la fonction de Artin}}, Ann. Sci. École Norm. Sup. (4), vol. 38, no. 6, (2005), 979-988.  

{{ :fr:xdeux.pdf | À propos de la fonction de Artin en dimension N≥2}}, C. R. Math. Acad. Sci. Paris, vol. 340, no. 8, (2005), 577-580.  (PDF)