Weil conjecture

22 examples (0.03 sec)
  • It is easy to check all parts of the Weil conjectures directly.
  • In quite a few cases, including that of the Weil conjectures, other methods have been found to prove such results unconditionally.
  • This is one of the steps used in the proof of the Weil conjectures.
  • He is known for work on the Weil conjectures, leading to a complete proof in 1973.
  • Perhaps Deligne's most famous contribution was his proof of the third and last of the Weil conjectures.
  • These give the first non-trivial cases of the Weil conjectures (proved by Hasse).
  • This has many applications, such as the proof of the Weil conjectures and the construction of representations of finite groups of Lie type.
  • Deligne won a Fields Medal in 1978 for his work on Weil conjectures.
  • The Weil conjecture on Tamagawa numbers proved resistant for many years.
  • In practice it is this generalization rather than the original Weil conjectures that is mostly used in applications, such as the hard Lefschetz theorem.
  • At that time the Weil conjectures were an outstanding motivation to research.
  • However, the Weil conjectures in their scope are more like a single Hilbert problem, and Weil never intended them as a programme for all mathematics.
  • This was one of the clues leading to the Weil conjectures.
  • As a first application, he proved the Weil conjecture on Tamagawa numbers for the large class of arbitrary simply connected Chevalley groups defined over the rational numbers.
  • The second observation, that the Tamagawa numbers of simply connected semisimple groups seem to be 1, became known as the Weil conjecture.
  • Even at an early stage in his work Serre had perceived a need to construct more general and refined cohomology theories to tackle the Weil conjectures.
  • It was used by to simplify Deligne's proof of the Weil conjectures.
  • Description: Proved the Riemann hypothesis for varieties over finite fields, settling the last of the open Weil conjectures.
  • The Weil conjectures had major applications to complete sums with domain restricted by polynomial conditions (i.e., along an algebraic variety over a finite field).
  • The Weil conjectures were formulated in the later 1940s as a set of mathematical problems in arithmetic geometry.
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