462 research outputs found
Residual Galois representations of elliptic curves with image contained in the normaliser of a non-split Cartan
It is known that if is a prime number and is an elliptic curve without complex multiplication, then the image of the mod Galois representation of is either the whole of , or is \emph{contained} in the normaliser of a non-split Cartan subgroup of . In this paper, we show that when , the image of is either , or the \emph{full} normaliser of a non-split Cartan subgroup. We use this to show the following result, partially settling a question of Najman. For , let denote the set of primes for which there exists an elliptic curve defined over and without complex multiplication admitting a degree isogeny defined over a number field of degree . We show that, for , we have I(d)=\{p\text{ prime}:p\leq d-1\}. $
Torsion of Q-curves over quadratic fields
We determine all the possible torsion groups of Q-curves overquadratic fields and determine which groups appear finitely andwhich appear infinitely often
Millimeter wave carbon nanotube gas sensor
This Letter reports experimental observations regarding the significant changes in the transmission modulus and phase of the propagating microwave signals up to 110 GHz in a micromachined coplanar waveguide supported on a dielectric membrane with a thickness of 1.4 m filled with a mixture of carbon nanotubes when exposed to nitrogen gas. These large shifts of amplitude and phase of microwave signals due to gas absorption represent the experimental basis on which a miniature wireless gas sensor could be implemented
Torsion of \Q-curves over quadratic fields
We find all the possible torsion groups of \Q-curves over quadratic fields
and determine which groups appear finitely and which appear infinitely often.Comment: 11 pages, to appear in Math. Res. Letter
Experimental determination of microwave attenuation and electrical permittivity of double-walled carbon nanotubes
The attenuation and the electrical permittivity of the double-walled carbon nanotubes (DWCNTs) were determined in the frequency range of 1–65 GHz. A micromachined coplanar waveguide transmission line supported on a Si membrane with a thickness of 1.4 µm was filled with a mixture of DWCNTs. The propagation constants were then determined from the S parameter measurements. The DWCNTs mixture behaves like a dielectric in the range of 1–65 GHz with moderate losses and an abrupt change of the effective permittivity that is very useful for gas sensor detection. ©2006 American Institute of Physic
Explicit height estimates for CM curves of genus 2
In this paper we make explicit the constants of Habegger and Pazuki's work
from 2017 on bounding the discriminant of cyclic Galois CM fields corresponding
to genus 2 curves with CM by them and potentially good reduction outside a
predefined set of primes. We also simplify some of the arguments
Torsion bounds for a fixed abelian variety and varying number field
Let be an abelian variety defined over a number field . For a finite
extension , the cardinality of the group of
torsion points in can be bounded in terms of the degree . We
study the smallest real number such that for any finite extension
and , we have , where the constant depends only on and
(and not ). Assuming the Mumford-Tate conjecture for , we
will show that agrees with the conjectured value of Hindry and
Ratazzi.Comment: 29 pages, comments very welcome
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