On the Finiteness of X for Motives Associated to Modular Forms
نویسنده
چکیده
Let f be a modular form of even weight on 0 (N) with associated motive M f . Let K be a quadratic imaginary eld satisfying certain standard conditions. We improve a result of Nekov a r and prove that if a rational prime p is outside a nite set of primes depending only on the form f , and if the image of the Heegner cycle associated with K in the p-adic intermediate Jacobian of M f is not divisible by p, then the p-part of the TateSafarevi c group of M f over K is trivial. An important ingredient of this work is an analysis of the behavior of \Kolyvagin test classes" at primes dividing the level N . In addition, certain complications, due to the possibility of f having a Galois conjugate self-twist, have to be dealt with. 1991 Mathematics Subject Classi cation: 11G18, 11F66, 11R34, 14C15.
منابع مشابه
Emergent Spacetime from Modular Motives
The program of constructing spacetime geometry from string theoretic modular forms is extended to Calabi-Yau varieties of dimensions two, three, and four, as well as higher rank motives. Modular forms on the worldsheet can be constructed from the geometry of spacetime by computing the L-functions associated to omega motives of Calabi-Yau varieties, generated by their holomorphic n−forms via Gal...
متن کاملMotives, modularity, and mirror symmetry
We consider certain families of Calabi-Yau orbifolds and their mirror partners constructed from Fermat hypersurfaces in weighted projective spaces. We use Fermat motives to interpret the topological mirror symmetry phenomenon. These Calabi-Yau orbifolds are defined over Q, and we can discuss the modularity of the associated Galois representations. We address the modularity question at the motiv...
متن کاملSome functional inequalities in variable exponent spaces with a more generalization of uniform continuity condition
Some functional inequalities in variable exponent Lebesgue spaces are presented. The bi-weighted modular inequality with variable exponent $p(.)$ for the Hardy operator restricted to non- increasing function which is$$int_0^infty (frac{1}{x}int_0^x f(t)dt)^{p(x)}v(x)dxleqCint_0^infty f(x)^{p(x)}u(x)dx,$$ is studied. We show that the exponent $p(.)$ for which these modular ine...
متن کاملOn certain finiteness questions in the arithmetic of modular forms
We investigate certain finiteness questions that arise naturally when studying approximations modulo prime powers of p-adic Galois representations coming from modular forms. We link these finiteness statements with a question by K. Buzzard concerning p-adic coefficient fields of Hecke eigenforms. Specifically, we conjecture that for fixed N , m, and prime p with p not dividing N , there is only...
متن کاملA fixed point approach to the Hyers-Ulam stability of an $AQ$ functional equation in probabilistic modular spaces
In this paper, we prove the Hyers-Ulam stability in$beta$-homogeneous probabilistic modular spaces via fixed point method for the functional equation[f(x+ky)+f(x-ky)=f(x+y)+f(x-y)+frac{2(k+1)}{k}f(ky)-2(k+1)f(y)]for fixed integers $k$ with $kneq 0,pm1.$
متن کامل