Pfister forms and a conjecture due to Colliot–Thelène in the mixed characteristic case
- Авторлар: Panin I.A.1, Tyurin D.N.1,2
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Мекемелер:
- St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
- Leonard Euler International Mathematical Institute at Saint Petersburg (SPB LEIMI)
- Шығарылым: Том 88, № 5 (2024)
- Беттер: 174-186
- Бөлім: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/265540
- DOI: https://doi.org/10.4213/im9566
- ID: 265540
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Аннотация
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 $K$.
Негізгі сөздер
Авторлар туралы
Ivan Panin
St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
Email: paniniv@gmail.com
Doctor of physico-mathematical sciences
Dimitrii Tyurin
St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences; Leonard Euler International Mathematical Institute at Saint Petersburg (SPB LEIMI)
Scopus Author ID: 57196744354
without scientific degree
Әдебиет тізімі
- K. Česnavičius, “Grothendieck–Serre in the quasi-split unramified case”, Forum Math. Pi, 10 (2022), e9, 30 pp.
- J.-L. Colliot-Thelène, “Formes quadratiques sur les anneaux semi-locaux reguliers”, Colloque sur les formes quadratiques, 2 (Montpellier, 1977), Bull. Soc. Math. France Mem., 59, 1979, 13–31
- M. Ojanguren, I. Panin, “Rationally trivial hermitian spaces are locally trivial”, Math. Z., 237:1 (2001), 181–198
- I. Panin, “Rationally isotropic quadratic spaces are locally isotropic”, Invent. Math., 176:2 (2009), 397–403
- I. Panin, Moving lemmas in mixed characteristic and applications
- I. Panin, On Grothendieck–Serre conjecture in mixed characteristic for $SL_{1,D}$
- I. Panin, K. Pimenov, “Rationally isotropic quadratic spaces are locally isotropic. II”, Doc. Math., 2010, Extra vol.: A. A. Suslin's 60th birthday, 515–523
- I. Panin, K. Pimenov, “Rationally isotropic quadratic spaces are locally isotropic. III”, Алгебра и анализ, 27:6 (2015), 234–241
- S. Scully, “The Artin–Springer theorem for quadratic forms over semi-local rings with finite residue fields”, Proc. Amer. Math. Soc., 146:1 (2018), 1–13
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