84 research outputs found
On the cohomology of plus/minus Selmer groups of supersingular elliptic curves in weakly ramified base fields
No full textLet be an elliptic curve and let be a prime of good
supersingular reduction. We generalize results due to Meng Fai Lim proving
Kida's formula and integrality results for characteristic elements of signed
Selmer groups along the cyclotomic -extension of weakly ramified
base fields .Comment: 29 page
Application of the magnetoresistive sensor for displacement measurement
No full textAn experimental rig was designed and successfully built to perform static and dynamic calibrations of the Philips magnetoresistive sensor. Characteristic of the sensor was also evaluated. A larger linear range can be achieved by having the sensor's transverse magnetic field pointing towards the stainless steel target. The measuring system behaves linearly with the variation of air gap from 0 to 0.46mm. The sensitivity of the measurement system is about 3 milivolts per micron of air gap variation. In terms of dynamic response, the magnetoresistive sensor performs as well as the commercially available Bently Nevada 5mm eddy curent displacement probe.Master of Science (Mechanics & Processing of Materials
Akashi series and Euler characteristics of signed Selmer groups of elliptic curves with semistable reduction at primes above
No full textOn order of vanishing of characteristic elements
No full textLet be a fixed odd prime. Let be an elliptic curve defined over a
number field with either good ordinary reduction or multiplicative reduction at
each prime of above . We shall study the characteristic element of the
Selmer group of over a -adic Lie extension. In particular, we relate the
order of vanishing of these characteristic element evaluated at Artin
representations to the Selmer coranks and their twists in the intermediate
subextensions of the -adic Lie extension.Comment: Several minor changes; added new reference
On the structure of even -groups of rings of algebraic integers
No full textIn this paper, we describe the higher even -groups of the ring of integers
of a number field in terms of class groups of an appropriate extension of the
number field in question. This is a natural extension of the previous
collective works of Browkin, Keune and Kolster, where they considered the case
of . We then revisit the Kummer's criterion of totally real fields as
generalized by Greenberg and Kida. In particular, we give an algebraic
-theoretical formulation of this criterion which we will prove using the
algebraic -theoretical results developed here.Comment: Some minor change
On the -divisibility of even -groups of the ring of integers of a cyclotomic field
No full textLet be a given positive odd integer and an odd prime. In this paper,
we shall give a sufficient condition when a prime divides the order of the
groups and
, where is a primitive th root of
unity. When is a -extension contained in for some
prime , we also establish a necessary and sufficient condition for the order
of to be divisible by . This generalizes a
previous result of Browkin which in turn has applications towards establishing
the existence of infinitely many cyclic extensions of degree which are -rational.Comment: Some minor corrections, some reogranization of the presentatio
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