In
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, the Shimura subgroup Σ(''N'') is a subgroup of the Jacobian of the
modular curve
In number theory and algebraic geometry, a modular curve ''Y''(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of the complex upper half-plane H by the action of a congruence subgroup Γ of the modular g ...
''X''
0(''N'') of level ''N'', given by the kernel of the natural map to the Jacobian of ''X''
1(''N''). It is named after
Goro Shimura
was a Japanese mathematician and Michael Henry Strater Professor Emeritus of Mathematics at Princeton University who worked in number theory, automorphic forms, and arithmetic geometry. He was known for developing the theory of complex multip ...
. There is a similar subgroup Σ(''N'',''D'') associated to
Shimura curves of quaternion algebras.
References
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Abelian varieties
Modular forms
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