# Dwork conjecture

In mathematics, the Dwork unit root zeta function, named after Bernard Dwork, is the L-function attached to the p-adic Galois representation arising from the p-adic etale cohomology of an algebraic variety defined over a global function field of characteristic p. The Dwork conjecture (1973) states that his unit root zeta function is p-adic meromorphic everywhere.[1] This conjecture was proved by Wan (2000).[2][3][4]

## References.

1. Dwork, Bernard (1973), "Normalized period matrices II", Annals of Mathematics 98 (1): 1–57, doi:10.2307/1970905 .
2. Wan, Daqing (1999), "Dwork's conjecture on unit root zeta functions", Annals of Mathematics 150 (3): 867–927, doi:10.2307/121058 .
3. Wan, Daqing (2000), "Higher rank case of Dwork's conjecture", Journal of the American Mathematical Society 13 (4): 807–852, doi:10.1090/S0894-0347-00-00339-8 .
4. Wan, Daqing (2000), "Rank one case of Dwork's conjecture", Journal of the American Mathematical Society 13 (4): 853–908, doi:10.1090/S0894-0347-00-00340-4 .