Modularity theorem information

rational numbers are related to modular forms in a particular way. Andrew Wiles and Richard Taylor proved the modularity theorem for semistable elliptic curves...

Hilbert modular forms. In 1986, upon reading Ken Ribet’s seminal work on Fermat’s Last Theorem, Wiles set out to prove the modularity theorem for semistable...

elliptic curve, something that could be called an elliptic modular curve. The modularity theorem, also known as the Taniyama–Shimura conjecture, asserts...

of number theory and the formulation of the modularity theorem in particular made it clear that modular forms are deeply implicated. Taniyama and Shimura...

module or modular in Wiktionary, the free dictionary. Module, modular and modularity may refer to the concept of modularity. They may also refer to: Modular design...

and modular forms. The resulting modularity theorem (at the time known as the Taniyama–Shimura conjecture) states that every elliptic curve is modular, meaning...

important theorems relating to modular arithmetic: Carmichael's theorem Chinese remainder theorem Euler's theorem Fermat's little theorem (a special...

19th century, and the proof of the modularity theorem in the 20th century. It is among the most notable theorems in the history of mathematics, and prior...

century. Manin–Drinfeld theorem Moduli stack of elliptic curves Modularity theorem Shimura variety, a generalization of modular curves to higher dimensions...

conjecture (later known as the modularity theorem) in the 1950s played a key role in the proof of Fermat's Last Theorem by Andrew Wiles in 1995. In 1990...

Michigan and at Columbia University. Conrad and others proved the modularity theorem, also known as the Taniyama-Shimura Conjecture. He proved this in...

universal algebra. Modular lattices arise naturally in algebra and in many other areas of mathematics. In these scenarios, modularity is an abstraction...

the modularity theorem) relating elliptic curves to modular forms. This connection would ultimately lead to the first proof of Fermat's Last Theorem in...

program modularity theorem Pythagorean triple Pell's equation Elliptic curve Nagell–Lutz theorem Mordell–Weil theorem Mazur's torsion theorem Congruent...

embedding theorem (category theory) Mittag-Leffler's theorem (complex analysis) Modigliani–Miller theorem (finance theory) Modularity theorem (number theory)...

as of September 2022[update]. The conjecture terminology may persist: theorems often enough may still be referred to as conjectures, using the anachronistic...

with integer coefficients. The famous modularity theorem tells us that all elliptic curves over Q are modular. Mappings also arise in connection with...

curves over rationals is called the Taniyama–Shimura conjecture or the modularity theorem whose statement he subsequently refined in collaboration with Goro...

Modern examples include the modularity theorem, which establishes an important connection between elliptic curves and modular forms (work on which led to...

geometry) Modularity theorem Moduli stack of elliptic curves Nagell–Lutz theorem Riemann–Hurwitz formula Wiles's proof of Fermat's Last Theorem Sarli, J...

the universal deformation space. A key step in Wiles's proof of the modularity theorem was to study the relation between universal deformation rings and...