Peter Bernd Schneider (born 9 January 1953 in Karlsruhe) is a German mathematician, specializing in the p-adic aspects of algebraic number theory, [1] arithmetic algebraic geometry, and representation theory. [2]
Peter Bernd Schneider (born 9 January 1953 in Karlsruhe) is a German mathematician, specializing in the p-adic aspects of algebraic number theory, [1] arithmetic algebraic geometry, and representation theory. [2]
Peter Schneider studied mathematics in Karlsruhe and Erlangen. After his Diplom in 1977 from the University of Erlangen-Nuremberg, [2] he was an assistant from 1977 to 1983 at the University of Regensburg. There he received in 1980 his PhD with advisor Jürgen Neukirch and dissertation Die Galoiscohomologie -adischer Darstellungen über Zahlkörpern (The Galois cohomology of -adic representations of number fields). [3] Schneider habilitated in 1982 at the University of Regensburg. He was a postdoc at Harvard University for the academic year 1983–1984 and a C2-professor at Heidelberg University for the academic year 1984–1985. He was a C4-professor from 1985 to 1994 at the University of Cologne and is since 1994 a C-4 professor at the University of Münster. [2]
His research includes Iwasawa theory, special values of -functions. and -adic representations (in the latter subject he has collaborated extensively with Jeremy Teitelbaum).
In 1992 Schneider, together with Christopher Deninger, Michael Rapoport and Thomas Zink, received the Gottfried Wilhelm Leibniz Prize for their work in using arithmetic-algebraic geometry to solve Diophantine equations. In 2006 he was an invited speaker with talk Continuous representation theory of p-adic Lie groups at the International Congress of Mathematicians in Madrid. In 2016 he was elected a member of the German National Academy of Sciences Leopoldina [4] and the Academia Europaea.
In representation theory and algebraic number theory, the Langlands program is a web of far-reaching and consequential conjectures about connections between number theory and geometry. Proposed by Robert Langlands, it seeks to relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and adeles. Widely seen as the single biggest project in modern mathematical research, the Langlands program has been described by Edward Frenkel as "a kind of grand unified theory of mathematics."
John Torrence Tate Jr. 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.
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, 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.
In mathematics, an Euler system is a collection of compatible elements of Galois cohomology groups indexed by fields. They were introduced by Kolyvagin (1990) in his work on Heegner points on modular elliptic curves, which was motivated by his earlier paper Kolyvagin (1988) and the work of Thaine (1988). Euler systems are named after Leonhard Euler because the factors relating different elements of an Euler system resemble the Euler factors of an Euler product.
In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties.
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, 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). 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.
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.
In mathematics, the local Langlands conjectures, introduced by Robert Langlands, are part of the Langlands program. They describe a correspondence between the complex representations of a reductive algebraic group G over a local field F, and representations of the Langlands group of F into the L-group of G. This correspondence is not a bijection in general. The conjectures can be thought of as a generalization of local class field theory from abelian Galois groups to non-abelian Galois groups.
In mathematics, a p-adic zeta function, or more generally a p-adic L-function, is a function analogous to the Riemann zeta function, or more general L-functions, but whose domain and target are p-adic. For example, the domain could be the p-adic integersZp, a profinite p-group, or a p-adic family of Galois representations, and the image could be the p-adic numbersQp or its algebraic closure.
In mathematics, p-adic Hodge theory is a theory that provides a way to classify and study p-adic Galois representations of characteristic 0 local fields with residual characteristic p. The theory has its beginnings in Jean-Pierre Serre and John Tate's study of Tate modules of abelian varieties and the notion of Hodge–Tate representation. Hodge–Tate representations are related to certain decompositions of p-adic cohomology theories analogous to the Hodge decomposition, hence the name p-adic Hodge theory. Further developments were inspired by properties of p-adic Galois representations arising from the étale cohomology of varieties. Jean-Marc Fontaine introduced many of the basic concepts of the field.
Jean-Marc Fontaine was a French mathematician. He was one of the founders of p-adic Hodge theory. He was a professor at Paris-Sud 11 University from 1988 to his death.
Pierre Colmez is a French mathematician, notable for his work on p-adic analysis.
In mathematics, Lafforgue's theorem, due to Laurent Lafforgue, completes the Langlands program for general linear groups over algebraic function fields, by giving a correspondence between automorphic forms on these groups and representations of Galois groups.
Christopher Deninger is a German mathematician at the University of Münster. Deninger's research focuses on arithmetic geometry, including applications to L-functions.
Peter Scholze is a German mathematician known for his work in arithmetic geometry. He has been a professor at the University of Bonn since 2012 and director at the Max Planck Institute for Mathematics since 2018. He has been called one of the leading mathematicians in the world. He won the Fields Medal in 2018, which is regarded as the highest professional honor in mathematics.
Lawrence Clinton Washington is an American mathematician at the University of Maryland who specializes in number theory.
Haruzo Hida is a Japanese mathematician, known for his research in number theory, algebraic geometry, and modular forms.
Uwe Jannsen is a German mathematician, specializing in algebra, algebraic number theory, and algebraic geometry.
| International | |
|---|---|
| National | |
| Academics | |
| Other | |
