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The main conjecture of Iwasawa theory was formulated as an assertion that two methods of defining p-adic L-functions ( by module theory, by interpolation ) should coincide, as far as that was well-defined.
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main and conjecture
Current wisdom has it that the massive coronal main sequence stars are late-A or early F stars, a conjecture that is supported both by observation and by theory.
The main difficulty in verifying Perelman's proof of the Geometrization conjecture was a critical use of his Theorem 7. 4 in the preprint ' Ricci Flow with surgery on three-manifolds '.
Remarkably, the main term in Riemann's formula was exactly the above integral, lending substantial weight to Gauss's conjecture.
Karl Rubin found a more elementary proof of the Mazur-Wiles theorem by using Kolyvagin's Euler systems, described in and, and later proved other generalizations of the main conjecture for imaginary quadratic fileds.
In each case, there is a main conjecture linking the tower to a p-adic L-function.
In 2002, Chris Skinner and Eric Urban claimed a proof of a main conjecture for GL ( 2 ).
This was a far-sighted conjecture for the time, given that the analytic continuation of L ( E, s ) there was only established for curves with complex multiplication, which were also the main source of numerical examples.
Combining this with the p-parity theorem by and the announced proof of the main conjecture of Iwasawa theory for GL ( 2 ) by, they conclude that a positive proportion of elliptic curves over Q have analytic rank zero, and hence, by, satisfy the Birch and Swinnerton-Dyer conjecture.
Algebraic K-groups are used in conjectures on special values of L-functions and the formulation of an non-commutative main conjecture of Iwasawa theory and in construction of higher regulators.
The main question in formulating the conjecture is to rule out this phenomenon.
The second conjecture of Conway and Norton then states that with V as above, for every element g of M, there is a genus zero subgroup K of PSL < sub > 2 </ sub >( R ), commensurable with the modular group Γ = PSL < sub > 2 </ sub >( Z ), such that is the normalized main modular function for K.
This led to Karl Rubin's new proof of the main conjecture of Iwasawa theory, considered simpler than the original proof due to Barry Mazur and Andrew Wiles.
These elements — named Beilinson elements after Alexander Beilinson who introduced them in — were used by Kazuya Kato in to prove one divisibility in Barry Mazur's main conjecture of Iwasawa theory for elliptic curves.
There are two main conjectures known as the Hadwiger conjecture or Hadwiger's conjecture:
The Hauptvermutung ( German for main conjecture ) of geometric topology is the conjecture that any two triangulations of a triangulable space have a common refinement, a single triangulation that is a subdivision of both of them.
main and theory
He also provided an algebraic definition of fundamental groups of schemes and more generally the main structures of a categorical Galois theory.
If the first theory is correct ( see above ), then the absence of cavalry removed the main Athenian tactical disadvantage, and the threat of being outflanked made it imperative to attack.
* Four main evidences of the Continental Drift theory
However it was only in 1927 that the shakta theory of seven main chakras, that has become most popular in the West, was introduced, largely through the translation of two Indian texts: the Sat-Cakra-Nirupana, and the Padaka-Pancaka, by Sir John Woodroffe, alias Arthur Avalon, in a book titled The Serpent Power.
The study of these complex linkages is the main goal of complex systems theory.
Acheson is one of the main proponents of this theory.
There are three main interpretations of Hume's theory of causation represented in the literature: ( 1 ) the logical positivist ; ( 2 ) the skeptical realist ; and ( 3 ) the quasi-realist.
One theory is that this was caused by a design fault in the ammunition loading system to the main gun turrets, so that an enemy hit on the turret set off an explosion in the magazine, thus sinking the ship.
For more information, see the main article on Bifurcation theory.
* Polyhedral skeletal electron pair theory for cluster compounds, including transition metals and main group elements such as boron including Wade's rules for polyhedral cluster compounds, including transition metals and main group elements and mixtures thereof.
In abstract algebra, field extensions are the main object of study in field theory.
In theory, the new Senate consisted of a broad national coalition, but in practice, with the main political groups unwilling to compromise and the most experienced politicians remaining outside it, the cabinet proved unable to solve any major local Finnish problems.
The other main theory, the sexual selection hypothesis, proposes that the long necks evolved as a secondary sexual characteristic, giving males an advantage in " necking " contests ( see below ) to establish dominance and obtain access to sexually receptive females.
According to a popular theory, Shakespeare's main source is believed to be an earlier play — now lost — known today as the Ur-Hamlet.
The theory for abelian locally compact groups is called Pontryagin duality ; it is considered to be in a satisfactory state, as far as explaining the main features of harmonic analysis goes.
At the Cowles Commission, Simon ’ s main goal was to link economic theory to mathematics and statistics.
The main theorist who pioneered the influential role-taking theory of hypnotism was Theodore Sarbin.
The main concepts of information theory can be grasped by considering the most widespread means of human communication: language.
In modern sociological theory, Marxist sociology is recognised as one of the main classical perspectives.
The main proponent of such a theory is Noam Chomsky, the originator of the generative theory of grammar, who has defined language as a particular set of sentences that can be generated from a particular set of rules.
There are three main categories of learning theory: behaviorism, cognitivism, and constructivism.
" At this stage, he seemed to have settled on leg theory, if not full bodyline, as his main tactic.
In general, the main results from this theory compare price-fixing methods across market structures, analyze the effect of a certain structure on welfare, and vary technological / demand assumptions in order to assess the consequences for an abstract model of society.
main and was
The town was about what Wilson expected: one main street with its rows of false-fronted buildings, a water tower, a few warehouses, a single hotel ; ;
That was the day that he had practically mopped up the main street of Big Sands with Aaron McBride, field boss for the Highlands Oil & Gas Company.
Fleischman with eight was to patrol the Leyte Gulf area, with his main task to get any kamikaze before they got to the ships.
Jean Bodin, writing in the sixteenth century, may have been the seminal thinker, but it was the vastly influential John Austin who set out the main lines of the concept as now understood.
He was ghost writer for Babe Ruth, whose main talent for literary composition was the signing of his autograph.
And it was his main present!!
The half-intensity diameter of the antenna beam was about 9', and the angle subtended by the moon included the entire main beam and part of the first side lobes.
The half-intensity diameter of the main lobe of the antenna was about 18'.5, and the brightness temperature was reduced by assuming a Gaussian shape for the antenna beam and a uniformly bright disk for the moon.
The issue was acute because the exiled Polish Government in London, supported in the main by Britain, was still competing with the new Lublin Government formed behind the Red Army.
But to return to the main line of our inquiry, it is doubtful that Utopia is still widely read because More was medieval or even because he was a martyr -- indeed, it is likely that these days many who read Utopia with interest do not even know that its author was a martyr.
The editor's main criticism of the trial was the haste with which it was conducted.
Like a wise gardener, Hardy pruned away the Shakespearian sonnets and songs, and the elements of meter and poetic diction to which his personal style was not suited, and let the main stock of his talent flourish.
Vermont's main railroad line was prostrate.
Because of this diversionary attack the main group that had been pinned down on the hill was able to surge forward again.
Since then he had worked at this and that, though some said his main interest was gambling.
At present the doctor's main concern was in seeing to it that Japanese salvage firms were not permitted to operate on the hulks of warships sunk too close inshore, because the work involved setting off nerve-shattering blasts at all hours.
He'd have to think, but the main thing, the imperative necessity, was to leave before Sam Bentley was up and about, and before Millie detained him with sympathy.
The damage caused by Sherman's March to the Sea through Georgia in 1864 was limited to a swath, but neither Lincoln nor his commanders saw destruction as the main goal, but rather defeat of the Confederate armies.
0.981 seconds.