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Cornelius Greither
Cornelius Greither (born 1956) is a German mathematician specialising in Iwasawa theory and the structure of Galois modules. Education and career Greither completed his PhD in 1983 at the Ludwig-Maximilians-Universität München under the supervision of Bodo Pareigis: his thesis bears the title ''Zum Kürzungsproblem kommutativer Algebren''. He habilitated in 1988 at same university, with thesis title ''Cyclic Galois extensions and normal bases''. In 1992, Greither proved the Iwasawa main conjecture for abelian number fields in the p=2 case. In 1999, together with D. R. Rapogle, K. Rubin, and A. Srivastav, he proved a converse to the Hilbert–Speiser theorem In mathematics, the Hilbert–Speiser theorem is a result on cyclotomic fields, characterising those with a normal integral basis. More generally, it applies to any finite abelian extension of , which by the Kronecker–Weber theorem are isomorph .... As of 2021, Greither is a full professor at t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iwasawa Theory
In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields. It began as a Galois module theory of ideal class groups, initiated by (), as part of the theory of cyclotomic fields. In the early 1970s, Barry Mazur considered generalizations of Iwasawa theory to abelian varieties. More recently (early 1990s), Ralph Greenberg has proposed an Iwasawa theory for motives. Formulation Iwasawa worked with so-called \Z_p-extensions - infinite extensions of a number field F with Galois group \Gamma isomorphic to the additive group of p-adic integers for some prime ''p''. (These were called \Gamma-extensions in early papers.) Every closed subgroup of \Gamma is of the form \Gamma^, so by Galois theory, a \Z_p-extension F_\infty/F is the same thing as a tower of fields :F=F_0 \subset F_1 \subset F_2 \subset \cdots \subset F_\infty such that \operatorname(F_n/F)\cong \Z/p^n\Z. Iwasawa studied classical Galois modules over F_n by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galois Module
In mathematics, a Galois module is a ''G''-module, with ''G'' being the Galois group of some extension of fields. The term Galois representation is frequently used when the ''G''-module is a vector space over a field or a free module over a ring in representation theory, but can also be used as a synonym for ''G''-module. The study of Galois modules for extensions of local or global fields and their group cohomology is an important tool in number theory. Examples *Given a field ''K'', the multiplicative group (''Ks'')× of a separable closure of ''K'' is a Galois module for the absolute Galois group. Its second cohomology group is isomorphic to the Brauer group of ''K'' (by Hilbert's theorem 90, its first cohomology group is zero). *If ''X'' is a smooth proper scheme over a field ''K'' then the ℓ-adic cohomology groups of its geometric fibre are Galois modules for the absolute Galois group of ''K''. Ramification theory Let ''K'' be a valued field (with valuat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ludwig-Maximilians-Universität München
The Ludwig Maximilian University of Munich (simply University of Munich or LMU; german: link=no, Ludwig-Maximilians-Universität München) is a public research university in Munich, Bavaria, Germany. Originally established as the University of Ingolstadt in 1472 by Duke Ludwig IX of Bavaria-Landshut, it is Germany's sixth-oldest university in continuous operation. In 1800, the university was moved from Ingolstadt to Landshut by King Maximilian I Joseph of Bavaria when the city was threatened by the French, before being transferred to its present-day location in Munich in 1826 by King Ludwig I of Bavaria. In 1802, the university was officially named Ludwig-Maximilians-Universität by King Maximilian I of Bavaria in honor of himself and Ludwig IX. LMU is currently the second-largest university in Germany in terms of student population; in the 2018/19 winter semester, the university had a total of 51,606 matriculated students. Of these, 9,424 were freshmen, while international ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Habilitation
Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a dissertation. The degree, abbreviated "Dr. habil." (Doctor habilitatus) or "PD" (for "Privatdozent"), is a qualification for professorship in those countries. The conferral is usually accompanied by a lecture to a colloquium as well as a public inaugural lecture. History and etymology The term ''habilitation'' is derived from the Medieval Latin , meaning "to make suitable, to fit", from Classical Latin "fit, proper, skillful". The degree developed in Germany in the seventeenth century (). Initially, habilitation was synonymous with "doctoral qualification". The term became synonymous with "post-doctoral qualification" in Germany in the 19th century "when holding a doctorate seemed no longer sufficient to guarantee a proficient transfe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iwasawa Main Conjecture
In mathematics, the main conjecture of Iwasawa theory is a deep relationship between ''p''-adic ''L''-functions and ideal class groups of cyclotomic fields, proved by Kenkichi Iwasawa for primes satisfying the Kummer–Vandiver conjecture and proved for all primes by . The Herbrand–Ribet theorem and the Gras conjecture are both easy consequences of the main conjecture. There are several generalizations of the main conjecture, to totally real fields,, CM fields, elliptic curves, and so on. Motivation was partly motivated by an analogy with Weil's description of the zeta function of an algebraic curve over a finite field in terms of eigenvalues of the Frobenius endomorphism on its Jacobian variety. In this analogy, * The action of the Frobenius corresponds to the action of the group Γ. * The Jacobian of a curve corresponds to a module ''X'' over Γ defined in terms of ideal class groups. * The zeta function of a curve over a finite field corresponds to a ''p''-adic ''L''- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abelian Number Field
In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local and global fields using objects associated to the ground field. Hilbert is credited as one of pioneers of the notion of a class field. However, this notion was already familiar to Kronecker and it was actually Weber who coined the term before Hilbert's fundamental papers came out. The relevant ideas were developed in the period of several decades, giving rise to a set of conjectures by Hilbert that were subsequently proved by Takagi and Artin (with the help of Chebotarev's theorem). One of the major results is: given a number field ''F'', and writing ''K'' for the maximal abelian unramified extension of ''F'', the Galois group of ''K'' over ''F'' is canonically isomorphic to the ideal class group of ''F''. This statement was generalized to the so called Artin reciprocity law; in the idelic language, writing ''CF ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karl Rubin
Karl Cooper Rubin (born January 27, 1956) is an American mathematician at University of California, Irvine as Edward O. Thorp, Thorp Professor of Mathematics. Between 1997 and 2006, he was a professor at Stanford, and before that worked at Ohio State University between 1987 and 1999. His research interest is in elliptic curves. He was the first mathematician (1986) to show that some elliptic curves over the rationals have finite Tate–Shafarevich groups. It is widely believed that these groups are always finite. Education and career Rubin graduated from Princeton University in 1976, and obtained his Ph.D. from Harvard in 1981. His thesis advisor was Andrew Wiles. He was a Putnam Fellow in 1974, and a Sloan Research Fellow in 1985. In 1988, Rubin received a National Science Foundation Presidential Young Investigator award, and in 1992 won the American Mathematical Society Cole Prize in number theory. In 2012 he became a fellow of the American Mathematical Society. Rubin's parent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilbert–Speiser Theorem
In mathematics, the Hilbert–Speiser theorem is a result on cyclotomic fields, characterising those with a normal integral basis. More generally, it applies to any finite abelian extension of , which by the Kronecker–Weber theorem are isomorphic to subfields of cyclotomic fields. :Hilbert–Speiser Theorem. A finite abelian extension has a normal integral basis if and only if it is tamely ramified over . This is the condition that it should be a subfield of where is a squarefree odd number. This result was introduced by in his Zahlbericht and by . In cases where the theorem states that a normal integral basis does exist, such a basis may be constructed by means of Gaussian periods. For example if we take a prime number , has a normal integral basis consisting of all the -th roots of unity other than . For a field contained in it, the field trace can be used to construct such a basis in also (see the article on Gaussian periods). Then in the case of squarefree and od ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universität Der Bundeswehr München
200px, Entrance to the university Bundeswehr University Munich (german: Universität der Bundeswehr München, UniBw München) is one of two research universities in Germany at federal level that both were founded in 1973 as part of the German Armed Forces (''Bundeswehr''). Originally called ''Hochschule der Bundeswehr München'' the institution was supposed to offer civilian academic education for military officers. As an uncommon feature amongst German universities Universität der Bundeswehr München unifies a more theoretical research university division and a more practical-oriented College of Applied Sciences branch. Today, the university has an increasing number of civilian and international students. The academic year at the university is structured in "trimesters" and not the usual semester, to offer intensive studies with more credit points per year. Very capable students can therefore achieve a bachelor's and a master's degree within less than four years, while this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1956 Births
Events January * January 1 – The Anglo-Egyptian Condominium ends in Sudan. * January 8 – Operation Auca: Five U.S. evangelical Christian missionaries, Nate Saint, Roger Youderian, Ed McCully, Jim Elliot and Pete Fleming, are killed for trespassing by the Huaorani people of Ecuador, shortly after making contact with them. * January 16 – Egyptian leader Gamal Abdel Nasser vows to reconquer Palestine. * January 25– 26 – Finnish troops reoccupy Porkkala, after Soviet troops vacate its military base. Civilians can return February 4. * January 26 – The 1956 Winter Olympics open in Cortina d'Ampezzo, Italy. February * February 11 – British spies Guy Burgess and Donald Maclean resurface in the Soviet Union, after being missing for 5 years. * February 14– 25 – The 20th Congress of the Communist Party of the Soviet Union is held in Moscow. * February 16 – The 1956 World Figure Skating Championships open in Garmisch, West Germany. * February 22 – Elvis P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
