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The spinor genus of the integral trace


Author: Guillermo Mantilla-Soler
Journal: Trans. Amer. Math. Soc. 369 (2017), 1611-1626
MSC (2010): Primary 11E12, 11R04, 11S99
DOI: https://doi.org/10.1090/tran/6723
Published electronically: June 2, 2016
MathSciNet review: 3581214
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Abstract: Let $ K$ be a number field of degree at least $ 3$. In this article we show that the genus of the integral trace form of $ K$ contains only one spinor genus. Additionally we show that exactly $ 43\%$ (resp. $ 29\%$, resp. $ 58\%$) of quadratic (resp. real quadratic, resp. imaginary quadratic) fields have the same property.


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Additional Information

Guillermo Mantilla-Soler
Affiliation: Departamento de Matemáticas, Universidad de los Andes, Carrera 1 N. 18A - 10, Bogotá, Colombia
Email: g.mantilla691@uniandes.edu.co

DOI: https://doi.org/10.1090/tran/6723
Received by editor(s): June 18, 2013
Received by editor(s) in revised form: June 24, 2014, December 1, 2014, and February 18, 2015
Published electronically: June 2, 2016
Article copyright: © Copyright 2016 American Mathematical Society