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John Tate (mathematician)
John Torrence Tate Jr. (March 13, 1925 – October 16, 2019) was an American mathematician, distinguished for many fundamental contributions in algebraic number theory, arithmetic geometry and related areas in algebraic geometry. He was awarded the Abel Prize in 2010. Biography Tate was born in Minneapolis, Minnesota. His father, John Tate Sr., was a professor of physics at the University of Minnesota, and a longtime editor of ''Physical Review''. His mother, Lois Beatrice Fossler, was a high school English teacher. Tate Jr. received his bachelor's degree in mathematics in 1946 from Harvard University, and entered the doctoral program in physics at Princeton University. He later transferred to the mathematics department and received his PhD in mathematics in 1950 after completing a doctoral dissertation, titled "Fourier analysis in number fields and Hecke's zeta functions", under the supervision of Emil Artin. Tate taught at Harvard for 36 years before joining the Univers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minneapolis
Minneapolis () is the largest city in Minnesota, United States, and the county seat of Hennepin County. The city is abundant in water, with thirteen lakes, wetlands, the Mississippi River, creeks and waterfalls. Minneapolis has its origins in timber and as the flour milling capital of the world. It occupies both banks of the Mississippi River and adjoins Saint Paul, the state capital of Minnesota. Prior to European settlement, the site of Minneapolis was inhabited by Dakota people. The settlement was founded along Saint Anthony Falls on a section of land north of Fort Snelling; its growth is attributed to its proximity to the fort and the falls providing power for industrial activity. , the city has an estimated 425,336 inhabitants. It is the most populous city in the state and the 46th-most-populous city in the United States. Minneapolis, Saint Paul and the surrounding area are collectively known as the Twin Cities. Minneapolis has one of the most extensive public par ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ken Ribet
Kenneth Alan Ribet (; born June 28, 1948) is an American mathematician working in algebraic number theory and algebraic geometry. He is known for the Herbrand–Ribet theorem and Ribet's theorem, which were key ingredients in the proof of Fermat's Last Theorem, as well as for his service as President of the American Mathematical Society from 2017 to 2019. He is currently a professor of mathematics at the University of California, Berkeley. Early life and education Kenneth Ribet was born in Brooklyn, New York to parents David Ribet and Pearl Ribet, both Jewish, on June 28, 1948. As a student at Far Rockaway High School, Ribet was on a competitive mathematics team, but his first field of study was chemistry. Ribet earned his bachelor's degree and master's degree from Brown University in 1969. In 1973, Ribet received his Ph.D. from Harvard University under the supervision of John Tate. Career After receiving his doctoral degree, Ribet taught at Princeton University for three years ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rigid Analytic Geometry
In mathematics, a rigid analytic space is an analogue of a complex analytic space over a nonarchimedean field. Such spaces were introduced by John Tate in 1962, as an outgrowth of his work on uniformizing ''p''-adic elliptic curves with bad reduction using the multiplicative group. In contrast to the classical theory of ''p''-adic analytic manifolds, rigid analytic spaces admit meaningful notions of analytic continuation and connectedness. Definitions The basic rigid analytic object is the ''n''-dimensional unit polydisc, whose ring of functions is the Tate algebra T_n, made of power series in ''n'' variables whose coefficients approach zero in some complete nonarchimedean field ''k''. The Tate algebra is the completion of the polynomial ring in ''n'' variables under the Gauss norm (taking the supremum of coefficients), and the polydisc plays a role analogous to that of affine ''n''-space in algebraic geometry. Points on the polydisc are defined to be maximal ideals in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tate Module
In mathematics, a Tate module of an abelian group, named for John Tate, is a module constructed from an abelian group ''A''. Often, this construction is made in the following situation: ''G'' is a commutative group scheme over a field ''K'', ''Ks'' is the separable closure of ''K'', and ''A'' = ''G''(''Ks'') (the ''Ks''-valued points of ''G''). In this case, the Tate module of ''A'' is equipped with an action of the absolute Galois group of ''K'', and it is referred to as the Tate module of ''G''. Definition Given an abelian group ''A'' and a prime number ''p'', the ''p''-adic Tate module of ''A'' is :T_p(A)=\underset A ^n/math> where ''A'' 'pn''is the ''pn'' torsion of ''A'' (i.e. the kernel of the multiplication-by-''pn'' map), and the inverse limit is over positive integers ''n'' with transition morphisms given by the multiplication-by-''p'' map ''A'' 'p''''n''+1→ ''A'' 'pn'' Thus, the Tate module encodes all the ''p''-power torsion of ''A''. It is equipped wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tate Conjecture
In number theory and algebraic geometry, the Tate conjecture is a 1963 conjecture of John Tate that would describe the algebraic cycles on a variety in terms of a more computable invariant, the Galois representation on étale cohomology. The conjecture is a central problem in the theory of algebraic cycles. It can be considered an arithmetic analog of the Hodge conjecture. Statement of the conjecture Let ''V'' be a smooth projective variety over a field ''k'' which is finitely generated over its prime field. Let ''k''s be a separable closure of ''k'', and let ''G'' be the absolute Galois group Gal(''k''s/''k'') of ''k''. Fix a prime number ℓ which is invertible in ''k''. Consider the ℓ-adic cohomology groups (coefficients in the ℓ-adic integers Zℓ, scalars then extended to the ℓ-adic numbers Qℓ) of the base extension of ''V'' to ''k''s; these groups are representations of ''G''. For any ''i'' ≥ 0, a codimension-''i'' subvariety of ''V'' (understood to be defined ov ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John H
John is a common English name and surname: * John (given name) * John (surname) John may also refer to: New Testament Works * Gospel of John, a title often shortened to John * First Epistle of John, often shortened to 1 John * Second Epistle of John, often shortened to 2 John * Third Epistle of John, often shortened to 3 John People * John the Baptist (died c. AD 30), regarded as a prophet and the forerunner of Jesus Christ * John the Apostle (lived c. AD 30), one of the twelve apostles of Jesus * John the Evangelist, assigned author of the Fourth Gospel, once identified with the Apostle * John of Patmos, also known as John the Divine or John the Revelator, the author of the Book of Revelation, once identified with the Apostle * John the Presbyter, a figure either identified with or distinguished from the Apostle, the Evangelist and John of Patmos Other people with the given name Religious figures * John, father of Andrew the Apostle and Saint Peter * Pope Jo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William C
William is a male given name of Germanic origin.Hanks, Hardcastle and Hodges, ''Oxford Dictionary of First Names'', Oxford University Press, 2nd edition, , p. 276. It became very popular in the English language after the Norman conquest of England in 1066,All Things William"Meaning & Origin of the Name"/ref> and remained so throughout the Middle Ages and into the modern era. It is sometimes abbreviated "Wm." Shortened familiar versions in English include Will, Wills, Willy, Willie, Bill, and Billy. A common Irish form is Liam. Scottish diminutives include Wull, Willie or Wullie (as in Oor Wullie or the play ''Douglas''). Female forms are Willa, Willemina, Wilma and Wilhelmina. Etymology William is related to the given name ''Wilhelm'' (cf. Proto-Germanic ᚹᛁᛚᛃᚨᚺᛖᛚᛗᚨᛉ, ''*Wiljahelmaz'' > German ''Wilhelm'' and Old Norse ᚢᛁᛚᛋᛅᚼᛅᛚᛘᛅᛋ, ''Vilhjálmr''). By regular sound changes, the native, inherited English form of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jerrold B
Jerrold or ''Jerold'' are masculine English given name variants of Gerald, a German language name meaning "rule of the spear" from the prefix ''ger-'' ("spear") and suffix ''-wald'' ("rule"). Jerrold was initially brought to Great Britain by the Normans. There are feminine nicknames, including Jeri. Jerrold is uncommon as a surname, although it was popular in the 11th and 12th century when biblical names were in style. People with the name Jerrold or its variants include: Given name * Jerold T. Hevener * Jerrold Immel, United States television composer * Jerrold E. Lomax, American architect. * Jerrold Northrop Moore (b. 1934), US-British musicologist * Jerrold Nadler, American politician from New York * Jerold Ottley Surname *Douglas William Jerrold (1803–1857), English dramatist and writer *James Douglas Jerrold (1847-1922), author *William Blanchard Jerrold (1826–1884), English journalist and author *Walter Jerrold (1865–1929), English writer and journalist ;Variant * D ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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