WEIGHT SPECTRAL SEQUENCES AND INDEPENDENCE OF $\ell$
For a variety over a local field, we show that the alternating sum of the traces of the composition of the actions of an element of the Weil group and an algebraic correspondence on the $\ell$-adic etale cohomology is independent of $\ell$. We prove the independence by establishing basic properties of weight spectral sequences.
AMS 2000 Mathematics subject classification: Primary 14G20. Secondary 11G25(Received September 18 2001)
(Accepted March 25 2003)
Key Words: semi-stable reduction; weight spectral sequence; independence of $\ell$; monodromy filtration; vanishing cycles.