51,886 research outputs found
On uniform lower bound of the Galois images associated to elliptic curves
Let p be a prime and K be a number field. Let rho_{E,p}:G_K \longrightarrow
Aut(T_p E)\cong GL_2(Z_p) be the Galois representation given by the Galois
action on the p-adic Tate module of an elliptic curve E over K. Serre showed
that the image of rho_{E,p} is open if E has no complex multiplication. For an
elliptic curve E over K whose j-invariant does not appear in an exceptional
finite set, we give an explicit uniform lower bound of the size of the image of
rho_{E,p}.Comment: 41 page
Mathematical Analysis of a Generalized Chiral Quark Soliton Model
A generalized version of the so-called chiral quark soliton model (CQSM) in
nuclear physics is introduced. The Hamiltonian of the generalized CQSM is given
by a Dirac type operator with a mass term being an operator-valued function.
Some mathematically rigorous results on the model are reported. The subjects
included are: (i) supersymmetric structure; (ii) spectral properties; (iii)
symmetry reduction; (iv) a unitarily equivalent model.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
Proof theory of weak compactness
We show that the existence of a weakly compact cardinal over the
Zermelo-Fraenkel's set theory is proof-theoretically reducible to iterations of
Mostowski collapsings and Mahlo operations
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