Jean-Pierre Serre is a French mathematician who has made contributions to algebraic topology, algebraic geometry and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the inaugural Abel Prize in 2003.
In mathematics, the Séminaire de Géométrie Algébrique du Bois Marie was an influential seminar run by French mathematician Alexander Grothendieck. It was a unique phenomenon of research and publication outside of the main mathematical journals that ran from 1960 to 1969 at the Institut des Hautes Études Scientifiques (IHÉS) near Paris. The seminar notes were eventually published in twelve volumes, all except one in the Springer Lecture Notes in Mathematics series.
In mathematics, a formal group law is a formal power series behaving as if it were the product of a Lie group. They were introduced by S. Bochner. The term formal group sometimes means the same as formal group law, and sometimes means one of several generalizations. Formal groups are intermediate between Lie groups and Lie algebras. They are used in algebraic number theory and algebraic topology.
Algebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called K-groups. These are groups in the sense of abstract algebra. They contain detailed information about the original object but are notoriously difficult to compute; for example, an important outstanding problem is to compute the K-groups of the integers.
In abstract algebra, an adelic algebraic group is a semitopological group defined by an algebraic group G over a number field K, and the adele ring A = A(K) of K. It consists of the points of G having values in A; the definition of the appropriate topology is straightforward only in case G is a linear algebraic group. In the case of G being an abelian variety, it presents a technical obstacle, though it is known that the concept is potentially useful in connection with Tamagawa numbers. Adelic algebraic groups are widely used in number theory, particularly for the theory of automorphic representations, and the arithmetic of quadratic forms.
Anatoly Ivanovich Maltsev was born in Misheronsky, near Moscow, and died in Novosibirsk, USSR. He was a mathematician noted for his work on the decidability of various algebraic groups. Malcev algebras, as well as Malcev Lie algebras are named after him.
Pierre Samuel was a French mathematician, known for his work in commutative algebra and its applications to algebraic geometry. The two-volume work Commutative Algebra that he wrote with Oscar Zariski is a classic. Other books of his covered projective geometry and algebraic number theory.
The Séminaire Nicolas Bourbaki is a series of seminars that has been held in Paris since 1948. It is one of the major institutions of contemporary mathematics, and a barometer of mathematical achievement, fashion, and reputation. It is named after Nicolas Bourbaki, a pseudonymous group of French and other mathematicians of variable membership.
Continuation of the Séminaire Nicolas Bourbaki programme, for the 1950s.
Continuation of the Séminaire Nicolas Bourbaki programme, for the 1960s.
In mathematics, Lazard's universal ring is a ring introduced by Michel Lazard in Lazard (1955) over which the universal commutative one-dimensional formal group law is defined.
In mathematics and specifically in topology, rational homotopy theory is a simplified version of homotopy theory for topological spaces, in which all torsion in the homotopy groups is ignored. It was founded by Dennis Sullivan and Daniel Quillen. This simplification of homotopy theory makes certain calculations much easier.
In mathematics, a Henselian ring is a local ring in which Hensel's lemma holds. They were introduced by Azumaya (1951), who named them after Kurt Hensel. Azumaya originally allowed Henselian rings to be non-commutative, but most authors now restrict them to be commutative.
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.
Luc Illusie is a French mathematician, specializing in algebraic geometry. His most important work concerns the theory of the cotangent complex and deformations, crystalline cohomology and the De Rham–Witt complex, and logarithmic geometry. In 2012, he was awarded the Émile Picard Medal of the French Academy of Sciences.
In mathematics, the Iwasawa algebra Λ(G) of a profinite group G is a variation of the group ring of G with p-adic coefficients that take the topology of G into account. More precisely, Λ(G) is the inverse limit of the group rings Zp(G/H) as H runs through the open normal subgroups of G. Commutative Iwasawa algebras were introduced by Iwasawa (1959) in his study of Zp extensions in Iwasawa theory, and non-commutative Iwasawa algebras of compact p-adic analytic groups were introduced by Lazard (1965).
Michel Demazure is a French mathematician. He made contributions in the fields of abstract algebra, algebraic geometry, and computer vision, and participated in the Nicolas Bourbaki collective. He has also been president of the French Mathematical Society and directed two French science museums.
In mathematics, Theory of Lie groups is a series of books on Lie groups by Claude Chevalley. The first in the series was one of the earliest books on Lie groups to treat them from the global point of view, and for many years was the standard text on Lie groups. The second and third volumes, on algebraic groups and Lie algebras, were written in French, and later reprinted bound together as one volume. Apparently further volumes were planned but not published, though his lectures on the classification of semisimple algebraic groups could be considered as a continuation of the series.
Yvette Amice was a French mathematician whose research concerned number theory and p-adic analysis. She was president of the Société mathématique de France.
Vincent Pilloni is a French mathematician, specializing in arithmetic geometry and the Langlands program.
