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Iwasawa considered the following tower of number fields:
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Iwasawa and considered
In the early 1970s, Barry Mazur considered generalizations of Iwasawa theory to abelian varieties.
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.
Iwasawa and tower
Iwasawa worked with so-called-extensions: infinite extensions of a number field with Galois group isomorphic to the additive group of p-adic integers for some prime p. Every closed subgroup of is of the form, so by Galois theory, a-extension is the same thing as a tower of fields such that.
Iwasawa and number
Tate's thesis ( 1950 ) on Fourier analysis in number fields has become one of the ingredients for the modern theory of automorphic forms and their L-functions, notably by its use of the adele ring, its self-duality and harmonic analysis on it ; independently and a little earlier, Kenkichi Iwasawa obtained a similar theory.
In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields.
Kenkichi Iwasawa ( Iwasawa Kenkichi, September 11, 1917 – October 26, 1998 ) was a Japanese mathematician who is known for his influence on algebraic number theory.
Iwasawa and fields
Via the theory of zeta integrals initiated by Kenkichi Iwasawa and by John Tate in Tate's thesis it is related to the study of the zeta function of global fields.
It began as a Galois module theory of ideal class groups, initiated by Kenkichi Iwasawa, in the 1950s, as part of the theory of cyclotomic fields.
Iwasawa is perhaps best known for introducing what is now called Iwasawa theory, which developed from researches on cyclotomic fields from the later parts of the 1950s.
considered and following
The following information on snakes varying greatly in size ( but all with less than a 10-foot maximum ) shows, when considered with the foregoing, that there is probably no correlation between the length of a snake and the time required for it to mature.
( Lauri Vaska, E. M. Sloane, J. W. DiLuzio ) In the absence of direct evidence to the contrary, decomposition of solvent alcohol and coordination of its fragments to the metal were not considered, following the above heretofore-accepted assumption in preparative coordination chemistry.
Phylogenetic analyses place these genera into the following groups ( not all of these are considered amoeboid ( or " amoebas ") by all sources ):
The Afroasiatic language family is usually considered to include the following branches:
In the following months, Hulbert and Spalding organized the National League by enlisting the four major teams in the East and the three other top teams in what was then considered to be the West.
The following mammals were once considered part of this group:
While the Minas Gerais was not considered likely to be replaced until the next century, it was nonetheless decommissioned in 2001 following the purchase of the French aircraft carrier Foch.
It seems that the Athenian playwright Aeschylus considered his participation at Marathon to be his greatest achievement in life ( rather than his plays ) since on his gravestone there was the following epigram:
When evaluating a coin, the following — often subjective — factors may be considered: 1 ) " eye appeal " or the aesthetic interest of the coin ; 2 ) dents on the rim ; 3 ) unsightly scratches or other blemishes on the surface of the coin ; 4 ) luster ; 5 ) toning ; 6 ) level of detail retained, where a coin with full details obviously is valued higher than one with worn details.
In response, the Solomon Islands began recruiting Cuban doctors in July 2007, while Papua New Guinea and Fiji considered following suit.
" Depending on one's point of view, all other uses can be considered derivatives of this use, including the following non-copular uses in English, as they all express a subset relationship.
Outside of Mexican-American communities, the term has been considered pejorative and takes on subjective view but usually consists of one or more of the following elements.
It should also be noted that the following techniques can also be considered fast protein liquid chromatography if no pressure is used to drive the mobile phase through the stationary phase.
1986 — In January 1986, following the rift between New Zealand and the USA in respect of the ANZUS security arrangements Prime Minister Tom Davis declared the Cook Islands a neutral country, because he considered that New Zealand ( which has control over the islands ' defence and foreign policy ) was no longer in a position to defend the islands.
The following languages have letters that contain diacritics that are considered independent letters distinct from those without diacritics.
The following languages have letter-diacritic combinations that are not considered independent letters.
To avoid debates about the possibility of in-vitro fertilization, artificial insemination, or cloning, the original Darwin Awards book applied the following " deserted island " test to potential winners: If the person were unable to reproduce when stranded on a deserted island with a fertile member of the opposite sex, he or she would be considered sterile.
In the following discussion the terms " sequence " and " vector " will be considered interchangeable.
As noted before, his first attempt was refused by Cauchy, but in February 1830 following Cauchy's suggestion he submitted it to the Academy's secretary Fourier, to be considered for the Grand Prix of the Academy.
The following year The Arte of English Poesie, attributed to George Puttenham, placed Oxford among a " crew " of courtier poets ; he also considered Oxford among the best comic playwrights of the day.
On a separate matter, PNG Trade and Industry Minister Paul Tiensten was quoted in Fiji Village on 21 February 2006 as saying that sanctions against Fiji were being considered, following a Fijian refusal of a PNG kava shipment and an earlier rejection of corned beef shipped from PNG.
As a result, the party was considered as a potential member of two other political coalitions, following the election.
Political scientist James McClellan, from the University of Virginia, considered Bacon to have had " a great following " in the American colonies.
Investments are generally not considered gambling when they meet the following criteria:
In the late 18th and early 19th centuries, following the French Revolution of 1789, a hugely influential grimoire was published under the title of the Grand Grimoire, which was considered particularly powerful because it involved conjuring and making a pact with the Devil's chief minister, Lucifugé Rofocale, in order to gain wealth from him.
considered and tower
When a third water tower was built next to the Okemah, Oklahoma set of Hot and Cold towers, the town briefly considered naming it " Running ", but eventually decided to use " Home of Woody Guthrie ".
Demolition of the tower was seriously considered, however it was subsequently restored, which took five years.
These include the Gerbrandy Tower, a structure that could be considered the tallest tower in Western Europe and during Christmas time the world's largest Christmas tree.
There is no clear definition of any difference between a tower block and a skyscraper, although a building with fifty or more storeys is generally considered a skyscraper.
The courthouse is still in use as a secondary location of county legal matters ( the city of Jackson having become the primary county seat ) and the Raymond courthouse is considered by many to be a prime example of southern Greek Revival architecture. Raymond water tower
Ruins of what is considered to be an 11th Century tower
For liability-related reasons, climbing the water tower is now considered a grave infraction.
The latter was built in Babylon during the 2nd millennium BC and was considered the tallest tower of the ancient world.
It is considered to be the tallest media tower in the world.
:* As ground level observation has limited view and more scope for distration, a raised viewing platform ( tower or walkway ) is " markedly superior " to ground or water level observation, and " the tower guard must be considered the foundation and most important part of the surveillance system ".
* The Cathedral has a great bell tower, standing at 57 m, which is considered the city's finest piece of art.
Although Plattenbauten are often considered to be typical of East Germany, the prefabricated construction method was used extensively in West Germany and elsewhere, particularly in public housing ( see tower block ).
Patients built the tower on the grounds, as this was considered therapeutic.
Both names are considered P-Celtic and may be derived from a Proto-Celtic root * mano-( alternately * meno-or * mono -) meaning either " thought " or " treading " ( another possibility being a derivative of another root * mono -, from Proto-Indo-European * men-meaning " to tower ", which gives us the Brythonic words for " mountain ").
The construction of the tower leaves viewers exposed to the elements and one reviewer considered that it reflected " the aerial perspective of modern warfare and the precariousness of the life below ".
In April 2007, the irregularities were straightened out, and the tower is now considered to be built legally.
The ancient Greek Helepolis, a massive siege tower which mounted catapults, could also be considered a weapons platform.
The Lutheran-Confessional Evangelical Church in the town square (" Praça " Arthur Gerhardt-Square ) was founded on 20 May 1866 and is considered the first evangelical church in Brazil to have a bell tower, as at that time only Catholic churches were permitted to build bell towers.
Watterson is composed of ten of these houses, ( five in each tower ), and each is considered — in terms of campus governance — to be its own residence hall.
Originally the tower was reached by a bascule drawbridge, usually considered to be drawn from contemporary French designs, such as those at Ferté-Milon and Vannes.
This tower was originally attached to an octagonal church, built in 1821 ; but when, in 1882, the edifice was considered too small for the town's population, the main building was demolished.
Plans are underway to clean up and restore the summit for public use, with demolition of the landmark tower being considered.
The test was considered a success, although there was insufficient separation distance when the tower jettisoned.
3.778 seconds.