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Zap. Nauchn. Sem. POMI, 2000, Volume 272, Pages 286–293 (Mi znsl1377)  

On a theorem of Grothendieck

I. A. Panin, A. L. Smirnov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: It is considered a smooth projective morphism $p\colon T\to S$ to a smooth variety $S$. It is proved, in particular, the following result. The total direct image $Rp_*(\mathbb Z/n\mathbb Z)$ of the constant étale sheaf $\mathbb Z/n\mathbb Z$ is locally for Zariski topology quasi-isomorphic to a bounded complex $\mathscr L$ on $S$ consisting of locally constant constructible étale $\mathbb Z/n\mathbb Z$-module sheaves.

Full text: PDF file (180 kB)

English version:
Journal of Mathematical Sciences (New York), 2003, 116:1, 3042–3046

Bibliographic databases:

UDC: 512.73
Received: 10.09.2000
Language:

Citation: I. A. Panin, A. L. Smirnov, “On a theorem of Grothendieck”, Problems in the theory of representations of algebras and groups. Part 7, Zap. Nauchn. Sem. POMI, 272, POMI, St. Petersburg, 2000, 286–293; J. Math. Sci. (N. Y.), 116:1 (2003), 3042–3046

Citation in format AMSBIB
\Bibitem{PanSmi00}
\by I.~A.~Panin, A.~L.~Smirnov
\paper On a theorem of Grothendieck
\inbook Problems in the theory of representations of algebras and groups. Part~7
\serial Zap. Nauchn. Sem. POMI
\yr 2000
\vol 272
\pages 286--293
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1377}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1811808}
\zmath{https://zbmath.org/?q=an:1070.14022}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2003
\vol 116
\issue 1
\pages 3042--3046
\crossref{https://doi.org/10.1023/A:1023471214286}


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