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- Geometric realizations of representations for
We construct a geometric realization of representations for PSL(2,Fp) by the defining ideals of rational models L(X(p)) of modular curves X(p) over Q, which gives rise to a Rosetta stone for geometric representations of PSL(2,Fp)
- Lecture 14: Modular curves over Q - websites. umich. edu
This is the first lecture on the arithmetic moduli theory of elliptic curves I began by explaining why the natural moduli problem for elliptic curves is not representable by a scheme I then proved (in a fair amount of detail) that the moduli problem of elliptic curves with full level 3 structure is representable by a scheme
- is the modular curve X (N) defined over Q? - MathOverflow
In most sources, the field of definition of the modular curve X(n)C (quotient of the upper half plane by the subgroup Γ(n) of SL2(Z) congruent to I mod n) is Q(μn), where μn is the group of n th roots of unity
- Modular Curves over Q i - Universiteit Utrecht
rves defined over Q(i) In this thesis, we will describe the arith-metically maximal subgroups corresponding to modular curves defined over Q(i) and attempt to compute all Q(i)-points on one of these curves Every modular curve either has infinitely many points over a given number field K or it h
- Modular Curves and the CM points on Modular Curves
Using this fact, we deduce that CM elliptic curves give rise to points on modular curves whose defining field is of relatively low degree Moreover, we can use CM elliptic curves to construct explicit points on modular curves for which we can analyze their defining fields
- AN ADELIC DESCRIPTION OF MODULAR CURVES - u-bordeaux. fr
The first chapter of this work reviews the classical, analytic definition of modular curves, which play a fundamental role in number theory As we have seen, to study equations over the integers it is usually necessary to study finite extensions Q ⊆ Q(α), which are called number fields
- Q-Curves and Their Manin Ideals - JSTOR
In this paper we propose a generalization of the Manin constant as a certain ideal (we call it the Manin ideal) attached to modular parametrizations of elliptic curves defined over number fields
- Modular Curves - The University of Warwick
2 2 1 Modular Curves as Riemann Surfaces 1 1 Modular curves as topological faces: r spaces
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