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Alexander Schmidt | |
|---|---|
| Born | 5 December 1965 |
| Nationality | German |
| Alma mater | University of Heidelberg |
| Scientific career | |
| Fields | Mathematics |
| Institutions | University of Heidelberg |
| Thesis | Positiv verzweigte Erweiterungen algebraischer Zahlkörper (1993) |
| Doctoral advisor | Kay Wingberg |
| Website | https://www.mathi.uni-heidelberg.de/~schmidt/ |
Alexander Schmidt (born 1965 [1] ) is a German mathematician at the University of Heidelberg. His research interests include algebraic number theory and algebraic geometry.
Schmidt attended the Heinrich Heinrich-Hertz-Gymnasium in East Berlin, a special school for mathematics. In 1984 he received the bronze medal at the International Mathematical Olympiad in Prague. [2] He studied mathematics at the Humboldt University in Berlin and was awarded the diploma in 1991. In 1993, he obtained his PhD at the University of Heidelberg by Kay Wingberg (Positive branched extensions of algebraic number fields). He then was a research assistant and later an assistant at the chair of Prof. Wingberg. He was also a Heisenberg fellow from 2002 to 2004. In 2000, he habilitated at the University of Heidelberg (with a thesis on the connection between algebraic cycle theory and higher-dimensional class field theory), was a private lecturer there, 2001 chair at the University of Cologne, and in 2004 became a professor at the University of Regensburg and is now a professor at the University of Heidelberg.
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 Kenkichi Iwasawa (1959), as part of the theory of cyclotomic fields. In the early 1970s, Barry Mazur considered generalizations of Iwasawa theory to abelian varieties. More recently, Ralph Greenberg has proposed an Iwasawa theory for motives.
In mathematics, Dirichlet's unit theorem is a basic result in algebraic number theory due to Peter Gustav Lejeune Dirichlet. It determines the rank of the group of units in the ring OK of algebraic integers of a number field K. The regulator is a positive real number that determines how "dense" the units are.
In mathematics, Galois cohomology is the study of the group cohomology of Galois modules, that is, the application of homological algebra to modules for Galois groups. A Galois group G associated to a field extension L/K acts in a natural way on some abelian groups, for example those constructed directly from L, but also through other Galois representations that may be derived by more abstract means. Galois cohomology accounts for the way in which taking Galois-invariant elements fails to be an exact functor.
In mathematics, Artin–Schreier theory is a branch of Galois theory, specifically a positive characteristic analogue of Kummer theory, for Galois extensions of degree equal to the characteristic p. Artin and Schreier (1927) introduced Artin–Schreier theory for extensions of prime degree p, and Witt (1936) generalized it to extensions of prime power degree pn.
In mathematics, the absolute Galois groupGK of a field K is the Galois group of Ksep over K, where Ksep is a separable closure of K. Alternatively it is the group of all automorphisms of the algebraic closure of K that fix K. The absolute Galois group is well-defined up to inner automorphism. It is a profinite group.
In mathematics, field arithmetic is a subject that studies the interrelations between arithmetic properties of a field and its absolute Galois group. It is an interdisciplinary subject as it uses tools from algebraic number theory, arithmetic geometry, algebraic geometry, model theory, the theory of finite groups and of profinite groups.
Jürgen Neukirch was a German mathematician known for his work on algebraic number theory.
In mathematics, especially in the areas of abstract algebra dealing with group cohomology or relative homological algebra, Shapiro's lemma, also known as the Eckmann–Shapiro lemma, relates extensions of modules over one ring to extensions over another, especially the group ring of a group and of a subgroup. It thus relates the group cohomology with respect to a group to the cohomology with respect to a subgroup. Shapiro's lemma is named after Arnold S. Shapiro, who proved it in 1961; however, Beno Eckmann had discovered it earlier, in 1953.
In algebraic number theory, Leopoldt's conjecture, introduced by H.-W. Leopoldt, states that the p-adic regulator of a number field does not vanish. The p-adic regulator is an analogue of the usual regulator defined using p-adic logarithms instead of the usual logarithms, introduced by H.-W. Leopoldt (1962).
In number theory, more specifically in p-adic analysis, Krasner's lemma is a basic result relating the topology of a complete non-archimedean field to its algebraic extensions.
Wolfgang Lück is a German mathematician who is an internationally recognized expert in algebraic topology.
In mathematics, Tate duality or Poitou–Tate duality is a duality theorem for Galois cohomology groups of modules over the Galois group of an algebraic number field or local field, introduced by John Tate (1962) and Georges Poitou (1967).
In algebraic topology, a transgression map is a way to transfer cohomology classes. It occurs, for example in the inflation-restriction exact sequence in group cohomology, and in integration in fibers. It also naturally arises in many spectral sequences; see spectral sequence#Edge maps and transgressions.
In mathematics, the Tsen rank of a field describes conditions under which a system of polynomial equations must have a solution in the field. The concept is named for C. C. Tsen, who introduced their study in 1936.
Joachim Cuntz is a German mathematician, currently a professor at the University of Münster.
Uwe Jannsen is a German mathematician, specializing in algebra, algebraic number theory, and algebraic geometry.
Gunter Malle is a German mathematician, specializing in group theory, representation theory of finite groups, and number theory.
Johannes Alfred Buchmann is a German computer scientist, mathematician and professor emeritus at the department of computer science of the Technische Universität Darmstadt.
Kay Wingberg is a German mathematician at the University of Heidelberg. His research interests include algebraic number theory, Iwasawa theory, arithmetic geometry and the structure of profinite groups.
Peter Bernd Schneider is a German mathematician, specializing in the p-adic aspects of algebraic number theory, arithmetic algebraic geometry, and representation theory.
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