Raskin's REU paper (Summer 2007)
on the Weil
for curves over finite fields is a
good source (******* ****) for
many of the details that
are missing from my
notes for Beilinson's lectures.
Dan Gardner's REU paper
(Summer 2007) elaborates on a comment made
during Beilinson's third lecture about the Kähler
analogue of the Riemann
hypothesis for smooth projective varieties over finite fields.