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Four-dimensional quadratic forms over \(\mathbb C(\!(t)\!)(X)\)

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Abstract

For quadratic forms in 4 variables defined over the rational function field in one variable over \(\mathbb C(\!(t)\!)\), the validity of the local-global principle for isotropy with respect to different sets of discrete valuations is examined.

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References

  1. Colliot-Thélène, J.-L., Parimala, R., Suresh, V.: Patching and local-global principles for homogeneous spaces over function fields of \(p\)-adic curves. Comment. Math. Helv. 87(4), 1011–1033 (2012)

    Article  MathSciNet  Google Scholar 

  2. Engler, A.J., Prestel, A.: Valued Fields. Springer, Berlin (2005)

    MATH  Google Scholar 

  3. Hartshorne, R.: Algebraic Geometry. Graduate Texts in Mathematics, vol. 52. Springer, New York, Heidelberg (1977)

  4. Lam, T.Y.: Introduction to Quadratic Forms over Fields. American Mathematical Society, Providence (2005)

    MATH  Google Scholar 

  5. Lichtenbaum, S.: Duality theorems for curves over \(p\)-adic fields. Invent. Math. 7(2), 120–136 (1969)

    Article  MathSciNet  Google Scholar 

  6. O’Meara, O.T.: Introduction to Quadratic Forms. Springer, Berlin (1973)

    Book  Google Scholar 

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Acknowledgements

The author wishes to thank David Leep, Suresh Venapally, Karim Johannes Becher, Gonzalo Manzano Flores, and Marco Zaninelli for many inspiring discussions and comments related to this article. This article is based on the author’s PhD-thesis, prepared under the supervision of Karim Johannes Becher (Universiteit Antwerpen) and Arno Fehm (Technische Universität Dresden) in the framework of a joint PhD at Universiteit Antwerpen and Universität Konstanz.

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  1. Departement Wiskunde, Universiteit Antwerpen, Middelheimlaan 1, 2020, Antwerpen, Belgium

    Parul Gupta

  2. IISER Pune, Dr. Homi Bhabha Road, Pashan, Pune, 411 008, India

    Parul Gupta

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  1. Parul Gupta
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Correspondence to Parul Gupta.

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This work was supported by the Fonds Wetenschappelijk Onderzoek – Vlaanderen (FWO) in the FWO Odysseus Programme (project ‘Explicit Methods in Quadratic Form Theory’), the Bijzonder Onderzoeksfonds (BOF), University of Antwerp (project BOF-DOCPRO-4, 2865), and the Science and Engineering Research Board (SERB), India (Grant CRG/2019/000271).

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Gupta, P. Four-dimensional quadratic forms over \(\mathbb C(\!(t)\!)(X)\). Arch. Math. 117, 369–374 (2021). https://doi.org/10.1007/s00013-021-01626-9

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  • DOI: https://doi.org/10.1007/s00013-021-01626-9

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