Holmstrom Weil conjectures

See Freitag-Kiehl, original articles of Dwork and Deligne, and lots of printed stuff in my office.

Kiehl and Weissauer: Weil conj, perverse sheaves, etc

Katz and Messing: Some consequences of the Riemann hypothesis for varieties over finite fields (1974)

Mazur: Extremely readable survey

SBS concluding post: http://sbseminar.wordpress.com/2010/06/10/motive-ating-the-weil-conjecture-proof/

http://mathoverflow.net/questions/72874/how-would-a-motivic-proof-of-the-riemann-hypothesis-over-finite-fields-go

http://mathoverflow.net/questions/33665/are-there-motivic-proofs-of-weil-conjectures-in-special-cases

http://sbseminar.wordpress.com/2010/05/03/the-weil-conjectures-the-approach-via-the-standard-conjectures/

http://sbseminar.wordpress.com/2010/04/12/the-weil-conjectures-and-the-problem-of-coefficients/

http://sbseminar.wordpress.com/2010/04/19/the-weil-conjectures-curves/

http://sbseminar.wordpress.com/2010/04/02/characteristic-zero-analogues-of-the-weil-conjectures-curves/

http://mathoverflow.net/questions/72834/what-exactly-does-the-weight-filtration-in-hodge-theory-have-to-do-with-the-weil

Some early writings:

• Chevalley, Bourbaki exp 3 and 9, for curves
• Exp 39, Delsarte
• Bourbaki exp 66 (Neron): Arithmetic on algebraic varieties

Irene had a book with some background.

The MathSciNet review of Deligne: La conjecture de Weil I, is very long and informative, with good historical references

nLab page on Weil conjectures