In mathematics, the Weil conjectures were highly influential proposals by André Weil (1949). They led to a successful multi-decade program to prove them...

The term Weil conjecture may refer to: The Weil conjectures about zeta functions of varieties over finite fields, proved by Dwork, Grothendieck, Deligne...

statement was known as the Taniyama–Shimura conjecture, Taniyama–Shimura–Weil conjecture, or the modularity conjecture for elliptic curves. The theorem states...

Poincaré conjecture), Fermat's Last Theorem, and others. Conjectures disproven through counterexample are sometimes referred to as false conjectures (cf....

Taniyama–Weil conjecture) based on a roughly formulated question of Taniyama at the 1955 Nikkō conference. His attitude towards conjectures was that one...

the Taniyama-Weil conjecture, itself an important result in number theory. For an elliptic curve over a number field K, the Hasse–Weil zeta function...

1949, André Weil posed the landmark Weil conjectures about the local zeta-functions of algebraic varieties over finite fields. These conjectures offered a...

mathematics, the standard conjectures about algebraic cycles are several conjectures describing the relationship of algebraic cycles and Weil cohomology theories...

André Weil found evidence supporting it, though not proving it; as a result the conjecture was often known as the Taniyama–Shimura–Weil conjecture.: 211–215 ...

be used to disprove the Taniyama–Shimura–Weil conjecture. Therefore, if the Taniyama–Shimura–Weil conjecture were true, no set of numbers capable of disproving...

geometry), motivic cohomology. Weil conjectures The Weil conjectures were three highly influential conjectures of André Weil, made public around 1949, on...

problems. One exception consists of three conjectures made by André Weil in the late 1940s (the Weil conjectures). In the fields of algebraic geometry, number...

1944) is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013...

to reduce the Ramanujan conjecture to the Weil conjectures that he later proved.　The more general Ramanujan–Petersson conjecture for holomorphic cusp forms...

Intelligencer *34, *76–78 (2012) Simone Pétrement (1988): 4–7  "The Weil Conjectures by Karen Olsson review – maths and mysticism". The Guardian. 2 August...

In mathematics, the Weil conjecture on Tamagawa numbers is the statement that the Tamagawa number τ ( G ) {\displaystyle \tau (G)} of a simply connected...

étale cohomology, the first example of a Weil cohomology theory, opened the way for a proof of the Weil conjectures, ultimately completed in the 1970s by...

cohomology to prove some of the Weil conjectures (Bernard Dwork had already managed to prove the rationality part of the conjectures in 1960 using p-adic methods)...

This is a list of notable mathematical conjectures. The following conjectures remain open. The (incomplete) column "cites" lists the number of results...

Tamagawa number τ(G) is defined to be the Tamagawa measure of G(A)/G(k). Weil's conjecture on Tamagawa numbers states that the Tamagawa number τ(G) of a simply...

Ramanujan conjecture, one was highly influential in later work. In particular, the connection of this conjecture with conjectures of André Weil in algebraic...

theorem (unproven at the time and then known as the "Taniyama–Shimura–Weil conjecture"). The modularity theorem involved elliptic curves, which was also...

(1979) and Vogan (1993) discuss the Langlands conjectures for more general groups. The Langlands conjectures for arbitrary reductive groups G are more complicated...

Grothendieck led to important foundational work, much of it motivated by the Weil conjectures. Two major foundational papers by Serre were Faisceaux Algébriques...

and elegant) proof of the Weil conjectures (which are proven by different means by Deligne), assuming the standard conjectures to hold. For example, the...

express the asymptotic behavior of the prime-counting function. The Weil's conjecture on Tamagawa numbers states that the Tamagawa number τ ( G ) {\displaystyle...

completes the proof. A proof is also possible assuming Weil's conjecture on Tamagawa numbers. The conjecture asserts for the case of the algebraic group SL2(R)...

formalism needed to solve deep problems of algebraic geometry, such as the Weil conjectures (the last of which was proved by Pierre Deligne). Strongly based on...

functions, and in particular for a proof of the first part of the Weil conjectures: the rationality of the zeta function of a variety over a finite field...

conjectures, originally proposed by André Weil in 1949 and proved by André Weil in the case of curves. Sato–Tate conjecture Schoof's algorithm Weil's...