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Tr. Mat. Inst. Steklova, 2003, Volume 241, Pages 254–264 (Mi tm399)  

On the Conjectures of Artin and Shafarevich–Tate

S. G. Tankeev

Vladimir State University

Abstract: For an arithmetic model $\pi\colon X\to\operatorname{Spec}A$ of a smooth projective variety $V$ over a number field $k$, the interrelations between the conjecture of Artin about the finiteness of $\mathrm{Br}(X)$ and the conjecture of Shafarevich–Tate about the finiteness of $III(\operatorname {Spec}A,\mathrm{Pic}^0(V))$ are studied.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2003, 241, 238–248

Bibliographic databases:
UDC: 512.6
Received in November 2002

Citation: S. G. Tankeev, “On the Conjectures of Artin and Shafarevich–Tate”, Number theory, algebra, and algebraic geometry, Collected papers. Dedicated to the 80th birthday of academician Igor' Rostislavovich Shafarevich, Tr. Mat. Inst. Steklova, 241, Nauka, MAIK Nauka/Inteperiodika, M., 2003, 254–264; Proc. Steklov Inst. Math., 241 (2003), 238–248

Citation in format AMSBIB
\Bibitem{Tan03}
\by S.~G.~Tankeev
\paper On the Conjectures of Artin and Shafarevich--Tate
\inbook Number theory, algebra, and algebraic geometry
\bookinfo Collected papers. Dedicated to the 80th birthday of academician Igor' Rostislavovich Shafarevich
\serial Tr. Mat. Inst. Steklova
\yr 2003
\vol 241
\pages 254--264
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm399}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2024055}
\zmath{https://zbmath.org/?q=an:1101.14031}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2003
\vol 241
\pages 238--248


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