# Dwork conjecture

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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.

- ↑ Dwork, Bernard (1973), "Normalized period matrices II",
*Annals of Mathematics***98**(1): 1–57, doi:10.2307/1970905. - ↑ Wan, Daqing (1999), "Dwork's conjecture on unit root zeta functions",
*Annals of Mathematics***150**(3): 867–927, doi:10.2307/121058. - ↑ 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. - ↑ 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.

Original source: https://en.wikipedia.org/wiki/Dwork conjecture.
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