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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2003, Volume 241, Pages 254–264 (Mi tm399)  
On the Conjectures of Artin and Shafarevich–Tate

S. G. Tankeev

Vladimir State University
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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 $\text{III}(\operatorname {Spec}A,\mathrm{Pic}^0(V))$ are studied.
Received in November 2002
Bibliographic databases:
UDC: 512.6
Language: Russian
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, Trudy 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 Trudy Mat. Inst. Steklova
\yr 2003
\vol 241
\pages 254--264
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm399}
\mathscinet{https://mathscinet.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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