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On the semisimplicity conjecture and Galois representations


Author: Lei Fu
Journal: Trans. Amer. Math. Soc. 353 (2001), 4357-4369
MSC (1991): Primary 14F20, 14G15
DOI: https://doi.org/10.1090/S0002-9947-01-02814-8
Published electronically: June 21, 2001
MathSciNet review: 1851174
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Abstract:

The semisimplicity conjecture says that for any smooth projective scheme $X_0$ over a finite field $\mathbf{F}_q$, the Frobenius correspondence acts semisimply on $H^i(X\otimes_{\mathbf{ F}_q} \mathbf{ F}, \overline{\mathbf{ Q}}_l)$, where $\mathbf{ F}$ is an algebraic closure of $\mathbf{ F}_q$. Based on the works of Deligne and Laumon, we reduce this conjecture to a problem about the Galois representations of function fields. This reduction was also achieved by Laumon a few years ago (unpublished).


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Additional Information

Lei Fu
Affiliation: Institute of Mathematics, Nankai University, Tianjin, P. R. China
Email: leifu@nankai.edu.cn

DOI: https://doi.org/10.1090/S0002-9947-01-02814-8
Keywords: $F$-semisimple representations, puncturely pure sheaves, $l$-adic Fourier transformations, perverse sheaves
Received by editor(s): November 5, 1999
Published electronically: June 21, 2001
Article copyright: © Copyright 2001 American Mathematical Society

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