There are several conjectures in mathematics by David Mumford.
- Mumford's conjecture about reductive groups, now called Haboush's theorem.
- The Mumford conjecture on the cohomology of the stable mapping class group, proved by Ib Madsen and Michael Weiss.
- The Manin-Mumford conjecture about Jacobians of curves, proved by Michel Raynaud.
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