Geodesic
Splitting of quadratic forms under some generic field extensions
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 9, Tome 289 (2002), pp. 267-276

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Let $F$ be a field, $\operatorname{char}\!F\ne2$, $\varphi$ and $\psi$ be anisotropic quadratic forms over $F$. Let $L$ be the generic field extension of $F$ such that $i(\psi_L)\ge2$. Under which conditions is the form $\varphi_L$ isotropic? We give the answer to this question in the cases where $\dim\varphi=5$, $\dim\psi=6$ and $\dim\varphi=6$, $\dim\psi=7$. 
@article{ZNSL_2002_289_a14,
     author = {A. S. Sivatski},
     title = {Splitting of quadratic forms under some generic field extensions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {267--276},
     publisher = {mathdoc},
     volume = {289},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a14/}
}
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A. S. Sivatski. Splitting of quadratic forms under some generic field extensions. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 9, Tome 289 (2002), pp. 267-276. http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a14/