Weil conjectures and their proof
Conjeturas de Weil y su prueba (cohomología étale, Deligne)
- Date
- 1949-1974 · confidence high
- Place
- Chicago and Bures-sur-Yvette (IHÉS)
- Credited to
- André Weil (statement, 1949); Alexander Grothendieck (étale cohomology, 1960s); Pierre Deligne (proof, 1974)
- People
- 👤 André Weil1906–1998
- Field
- Knowledge & symbols
What was discovered
Statements about the number of solutions of polynomial equations over finite fields, analogous to the Riemann hypothesis, whose proof required rebuilding algebraic geometry with schemes and étale cohomology.
Grothendieck's revolution (EGA, SGA) is considered the greatest refounding of a branch of mathematics in the 20th century.
What it led to
- modern algebraic geometry (schemes)
- the Langlands programme
- elliptic-curve cryptography
- algebraic-geometric codes
Built on
- Riemann hypothesis1859
- Category theory1945
- Grothendieck topologyc. 1962
- Hasse (elliptic curves, 1933)
Made possible
- Langlands program1967
- point counting in elliptic-curve cryptography