Auel, Asher; Suresh, V. Failure of the local-global principle for isotropy of quadratic forms over function fields. (English) Zbl 07918114 Algebra Number Theory 18, No. 8, 1497-1513 (2024). Reviewer: Stefan Gille (Edmonton) MSC: 11E04 11R58 12G05 14G12 14H52 14J32 14J40 19D45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Linh, Nguyen Manh Arithmetics of homogeneous spaces over \(p\)-adic function fields. (English) Zbl 1540.14055 J. Lond. Math. Soc., II. Ser. 109, No. 1, Article ID e12842, 56 p. (2024). Reviewer: Felipe Gambardella (Paris) MSC: 14G05 14G12 11E72 × Cite Format Result Cite Review PDF Full Text: DOI arXiv OA License
Kuznetsov, Alexander; Prokhorov, Yuri Rationality over nonclosed fields of Fano threefolds with higher geometric Picard rank. (English) Zbl 1536.14010 J. Inst. Math. Jussieu 23, No. 1, 207-247 (2024). Reviewer: Ivo M. Michailov (Shumen) MSC: 14E08 14J45 14E30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wu, Han There are genus one curves violating Hasse principle over every number field. (English) Zbl 07799749 J. Algebra 643, 76-85 (2024). MSC: 14H45 11G05 11D09 14G05 × Cite Format Result Cite Review PDF Full Text: DOI
Wu, Han Arithmetic of Châtelet surfaces under extensions of base fields. (English) Zbl 07784976 Ramanujan J. 62, No. 4, 997-1010 (2023). MSC: 11G35 14G12 14G25 14G05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kuznetsov, Alexander; Prokhorov, Yuri Rationality of Fano threefolds over non-closed fields. (English) Zbl 1525.14022 Am. J. Math. 145, No. 2, 335-411 (2023). Reviewer: Anton Fonarev (Moskva) MSC: 14Exx 14E08 14J45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Pieropan, Marta On rationally connected varieties over \(C_1\) fields of characteristic 0. (English) Zbl 1515.14040 Algebra Number Theory 16, No. 8, 1811-1844 (2022). Reviewer: Qixiao Ma (Hannover) MSC: 14G05 14M22 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mitankin, Vladimir; Salgado, Cecília Genus one fibrations and vertical Brauer elements on del Pezzo surfaces of degree 4. (English) Zbl 1482.14024 J. Number Theory 236, 463-478 (2022). MSC: 14G05 11G35 14F22 14J26 11D09 14D10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Creutz, Brendan; Viray, Bianca Degree and the Brauer-Manin obstruction. (English) Zbl 1408.14086 Algebra Number Theory 12, No. 10, 2445-2470 (2018). Reviewer: Damián Gvirtz (London) MSC: 14G05 11G35 14F22 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Liedtke, Christian Morphisms to Brauer-Severi varieties, with applications to del Pezzo surfaces. (English) Zbl 1406.14015 Bogomolov, Fedor (ed.) et al., Geometry over nonclosed fields. Proceedings of the Simons symposium, March 22–28, 2015. Cham: Springer (ISBN 978-3-319-49762-4/hbk; 978-3-319-49763-1/ebook). Simons Symposia, 157-196 (2017). MSC: 14F22 14A10 14J45 14G27 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Harpaz, Yonatan; Wittenberg, Olivier On the fibration method for zero-cycles and rational points. (English) Zbl 1342.14052 Ann. Math. (2) 183, No. 1, 229-295 (2016). Reviewer: B. Z. Moroz (Bonn) MSC: 14G05 14D06 14G25 14D10 14F22 11G35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Charles, François; Pirutka, Alena The Tate conjecture for four-dimensional cubics. (La conjecture de Tate entière pour les cubiques de dimension quatre.) (French. English summary) Zbl 1316.14084 Compos. Math. 151, No. 2, 253-264 (2015). Reviewer: Fumio Hazama (Hatoyama) MSC: 14J70 14C25 14G15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ciperiani, Mirela; Krashen, Daniel Relative Brauer groups of genus 1 curves. (English) Zbl 1259.14020 Isr. J. Math. 192, Part B, 921-949 (2012). Reviewer: Stefan Schröer (Düsseldorf) MSC: 14F22 11G05 16K20 16K50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Asok, Aravind; Haesemeyer, Christian Stable \(\mathbb A^1\)-homotopy and \(R\)-equivalence. (English) Zbl 1244.14016 J. Pure Appl. Algebra 215, No. 10, 2469-2472 (2011). Reviewer: Gereon Quick (Cambridge) MSC: 14F42 14G05 55P42 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Poonen, B. Curves over every global field violating the local-global principle. (English) Zbl 1294.11108 J. Math. Sci., New York 171, No. 6, 782-785 (2010) and Zap. Nauchn. Semin. POMI 377, 141-147 (2010). Reviewer: Roberto Dvornicich (Pisa) MSC: 11G30 14G05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Poonen, Bjorn Existence of rational points on smooth projective varieties. (English) Zbl 1183.14032 J. Eur. Math. Soc. (JEMS) 11, No. 3, 529-543 (2009). Reviewer: Boris Kunyavskii (Ramat Gan) MSC: 14G05 11G35 11U05 14G25 14J20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Clark, Pete L. On elementary equivalence, isomorphism and isogeny. (English) Zbl 1106.12003 J. Théor. Nombres Bordx. 18, No. 1, 29-58 (2006). Reviewer: Detlev Hoffmann (Nottingham) MSC: 12F20 11E04 11G05 11R58 12L12 14M15 16K50 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
Heath-Brown, Roger; Skorobogatov, Alexei [Heath-Brown, D. R.] Rational solutions of certain equations involving norms. (English) Zbl 1023.11033 Acta Math. 189, No. 2, 161-177 (2002). Reviewer: B.Kunyavskii (Ramat Gan) MSC: 11G35 14G05 11P55 14G25 × Cite Format Result Cite Review PDF Full Text: DOI
Harari, David Hasse principle and weak approximation on certain hypersurfaces. (Principe de Hasse et approximation faible sur certaines hypersurfaces.) (French) Zbl 0870.14014 Ann. Fac. Sci. Toulouse, VI. Sér., Math. 4, No. 4, 731-762 (1995). Reviewer: B.Kunyavskii (Ramat Gan) MSC: 14G05 14G25 14J70 14F22 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
Harari, David Fibration method and Manin obstruction. (Méthode des fibrations et obstruction de Manin.) (French) Zbl 0847.14001 Duke Math. J. 75, No. 1, 221-260 (1994). Reviewer: A.N.Parshin (Moskva) MSC: 14B12 14F22 14G25 × Cite Format Result Cite Review PDF Full Text: DOI
Skorobogatov, Alexei N. On a theorem of Enriques–Swinnerton-Dyer. (English) Zbl 0811.14020 Ann. Fac. Sci. Toulouse, VI. Sér., Math. 2, No. 3, 429-440 (1993). MSC: 14G05 14J99 14M15 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
Colliot-Thélène, Jean-Louis; Sansuc, Jean-Jacques La descente sur les variétés rationnelles. II. (The descent on rational varieties. II). (French) Zbl 0659.14028 Duke Math. J. 54, 375-492 (1987). Reviewer: G.Faltings MSC: 14M20 14G05 14G25 14J25 × Cite Format Result Cite Review PDF Full Text: DOI