On a functorial isomorphism in the derived category of $l$-adic sheaves

V.V.Lyubashenko

For a vector bundle $h\colon{}E\to B$ of dimension $d$ over the algebraic closure of a finite field we prove that the functor $\bar Rh_!\circ h^*\colon{}D^b(B,{\Bbb Q}_\ell)\to D^b(B,{\Bbb Q}_\ell)$ is isomorphic to the (twisted) shift functor $[-2d](-d)$.

1. A. A. Beilinson, J. Bernstein, and P. Deligne, Faisceaux pervers, Soc. Math. de France, Astérisque, 100 (1982).

2. J. Bernstein and V. Lunts, Equivariant sheaves and functors, Lecture Notes in Math., vol. 1578, Springer, Berlin, Heidelberg, 1994.

3. P. Deligne, Cohomologie à supports propres, in book: Théorie des Topos et Cohomologie Etale des Schémas (SGA 4) (M. Artin, A. Grothendieck, and J. L. Verdier eds.) Lect. Notes in Math., no. 305, Springer-Verlag, Berlin, Heidelberg, New York, 1973, 250–480.

4. R. Hartshorne, Algebraic geometry, Graduate texts in mathematics, vol. 52, Springer-Verlag, New York, Heidelberg, Berlin, 1977.

5. J. S. Milne, Etale cohomology, Princeton Mathematical Series, vol. 33, Princeton Univ. Press, Princeton, New Jersey, 1980.

	On a functorial isomorphism in the derived category of $l$-adic sheaves
Author	V.V.Lyubashenko lub@imath.kiev.ua Institute of Mathematics, National ,Academy of Sciences of Ukraine, , 3, Tereshchenkivska st., Kyiv-4, ,01601 MSP, Ukraine
Abstract	For a vector bundle $h\colon{}E\to B$ of dimension $d$ over the algebraic closure of a finite field we prove that the functor $\bar Rh_!\circ h^*\colon{}D^b(B,{\Bbb Q}_\ell)\to D^b(B,{\Bbb Q}_\ell)$ is isomorphic to the (twisted) shift functor $[-2d](-d)$.
Keywords	vector bundles over finite fields, algebraic closure of finite fields, vector bundles over finite fields, algebraic closure of finite fields
DOI	doi:10.30970/ms.14.2.115-120
Reference	1. A. A. Beilinson, J. Bernstein, and P. Deligne, Faisceaux pervers, Soc. Math. de France, Astérisque, 100 (1982). 2. J. Bernstein and V. Lunts, Equivariant sheaves and functors, Lecture Notes in Math., vol. 1578, Springer, Berlin, Heidelberg, 1994. 3. P. Deligne, Cohomologie à supports propres, in book: Théorie des Topos et Cohomologie Etale des Schémas (SGA 4) (M. Artin, A. Grothendieck, and J. L. Verdier eds.) Lect. Notes in Math., no. 305, Springer-Verlag, Berlin, Heidelberg, New York, 1973, 250–480. 4. R. Hartshorne, Algebraic geometry, Graduate texts in mathematics, vol. 52, Springer-Verlag, New York, Heidelberg, Berlin, 1977. 5. J. S. Milne, Etale cohomology, Princeton Mathematical Series, vol. 33, Princeton Univ. Press, Princeton, New Jersey, 1980.
Pages	115-120
Volume	14
Issue	2
Year	2000
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html