Moduli stack of elliptic curves information

In mathematics, the moduli stack of elliptic curves, denoted as M 1 , 1 {\displaystyle {\mathcal {M}}_{1,1}} or M ell {\displaystyle {\mathcal {M}}_{\textrm...

constructing moduli spaces as algebraic stacks from moduli functors Moduli of algebraic curves Moduli stack of elliptic curves Moduli spaces of K-stable Fano...

and the moduli stack of elliptic curves. Originally, they were introduced by Alexander Grothendieck to keep track of automorphisms on moduli spaces, a...

a moduli space of (algebraic) curves is a geometric space (typically a scheme or an algebraic stack) whose points represent isomorphism classes of algebraic...

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

\Gamma ={\text{SL}}_{2}(\mathbb {Z} )} are sections of a line bundle on the moduli stack of elliptic curves. A modular function is a function that is invariant...

1\mod N,c\equiv 0\mod N\right\}.} These curves have a direct interpretation as moduli spaces for elliptic curves with level structure and for this reason...

after many years of effort. Level structure (algebraic geometry) Moduli stack of elliptic curves Drinfeld, Vladimir (1974), "Elliptic modules", Matematicheskii...

{Spectra}}} over the site of affine schemes flat over the moduli stack of elliptic curves. The desire to get a universal elliptic cohomology theory by taking...

natural generalization of elliptic curves, including algebraic tori in higher dimensions. Just as elliptic curves have a natural moduli space M 1 , 1 {\displaystyle...

the moduli stack of (generalized) elliptic curves. This theory has relations to the theory of modular forms in number theory, the homotopy groups of spheres...

which are a family of elliptic curves degenerating to a rational curve with a cusp. One of the most important properties of stable curves is the fact that...

natural moduli problem or, in the precise language, there is no natural moduli stack that would be an analog of moduli stack of stable curves. An algebraic...

is Zariski dense there). All elliptic curves are the Jacobian of themselves, hence the moduli stack of elliptic curves M 1 , 1 {\displaystyle {\mathcal...

rational curves, i.e. the curve is birational to the projective line P 1 {\displaystyle \mathbb {P} ^{1}} . (b) g = 1 {\displaystyle g=1} . Elliptic curves, i...

Differential of the first kind Jacobian variety Generalized Jacobian Moduli of algebraic curves Hurwitz's theorem on automorphisms of a curve Clifford's...

completed his PhD in 1961, with a thesis entitled Existence of the moduli scheme for curves of any genus. He married Erika, an author and poet, in 1959 and...

representations of the étale fundamental group of an algebraic curve to objects of the derived category of l-adic sheaves on the moduli stack of vector bundles...

work also gave rise to the ideas of an algebraic space and algebraic stack, and has proved very influential in moduli theory. He also has made important...

idea that the moduli problem is to express the algebraic structure naturally coming with a set (say of isomorphism classes of elliptic curves). The result...

hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscates and Cassini ovals. These are plane algebraic curves. A point of the plane lies...

the first-order deformation space of X. This is the basic calculation needed to show that the moduli space of curves of genus g has dimension 3 g − 3 {\displaystyle...

the construction of moduli spaces but are not always possible in the smaller category of schemes, such as taking the quotient of a free action by a finite...

because it implies many moduli spaces encountered in the wild are Noetherian, such as the Moduli of algebraic curves and Moduli of stable vector bundles...