# References for general Hasse-Weil zeta function

Most research on the Hasse-Weil zeta function focuses on some particular type of algebraic variety, and general surveys usually deal mostly with the better understood elliptic curve case.

I am looking for references about the Hasse-Weil zeta for arbitrary variety and number field, particularly analytic continuation and functional equation (this is, not focused on special values or zeroes).

Also, I have Serre's "Facteurs locaux", so probably anything published before 1970 would be redundant.

Edit. For future reference, Ivan Fesenko's research, particularly "Analysis on arithmetic schemes" parts I, II and III, fit perfectly in this context. Also, some older papers like Alexei Parshin, for example, "Chern classes, adeles and L-functions".

• I do not know any other coherent reference than "facteurs locaux".... – Damian Rössler Jan 25 '15 at 13:28
• There is a reason why much of the literature deals with elliptic curves and/or abelian varieties: the analytic continuation and functional equation of the $L$-function is a wide open problem for arbitrary varieties. – Olivier Feb 6 '15 at 14:08