Geodesic
Pfister forms and a~conjecture due~to~Colliot--Th\'{e}l\`{e}ne in the mixed characteristic case
Izvestiya. Mathematics , Tome 88 (2024) no. 5, pp. 977-987

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Let $R$ be a regular local ring of mixed characteristic $(0,p)$, where $p\neq 2$ is a prime number. Suppose that the quotient ring $R/pR$ is also regular. We fix a non-degenerate Pfister form $Q(T_{1},\ldots,T_{2^{m}})$ over $R$ and an invertible element $c$ in $R$. Then the equation $Q(T_{1},\ldots,T_{2^{m}})=c$ has a solution over $R$ if and only if it has a solution over the fraction field $K$.
Keywords: quadratic form, Colliot–Thélène conjecture, mixed characteristic.
Mots-clés : Pfister form 
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     author = {I. A. Panin and D. N. Tyurin},
     title = {Pfister forms and a~conjecture {due~to~Colliot--Th\'{e}l\`{e}ne} in the mixed characteristic case},
     journal = {Izvestiya. Mathematics },
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I. A. Panin; D. N. Tyurin. Pfister forms and a~conjecture due~to~Colliot--Th\'{e}l\`{e}ne in the mixed characteristic case. Izvestiya. Mathematics , Tome 88 (2024) no. 5, pp. 977-987. http://geodesic.mathdoc.fr/item/IM2_2024_88_5_a4/