Definitions

1. Serre is the only laureate of each of the Fields Medal and the Wolf and Abel Prizes.
2. Serre is awarded a Fields Medal for his work on spectral sequences and his work developing complex variable theory in terms of sheaves. (Web site)
3. Serre was awarded the Fields Medal in 1954, and was the first recipient of the Abel Prize in 2003. (Web site)
4. Serre was awarded his doctorate from the Sorbonne in 1951.
5. Jean-Pierre Serre (born 15 September 1926) is a French mathematician in the fields of algebraic geometry, number theory and topology.

Writing Mathematics

1. David Goss has some advice about writing mathematics, which apparently owes something to Serre.

Written

1. These varieties have been called 'varieties in the sense of Serre', since Serre 's foundational paper FAC on sheaf cohomology was written for them. (Web site)

Published

1. Many of his results were not immediately published and were written up by Jean-Pierre Serre. (Web site)

Algebraic

1. An algebraic (and much easier) version of this theorem was proved by Serre. (Web site)

Research Papers

1. Others are research papers by authors such as Coleman and Mazur, Goncharov, Gross and Serre.

Groups

1. It is a theorem of Serre that these groups are finite if k 0.

Mathematics

1. Over many years, Serre has published many highly influential texts covering a wide range of mathematics. (Web site)
2. How to write mathematics badly a public lecture by Jean-Pierre Serre on writing mathematics. (Web site)

Fields Medal

1. In 1954, Jean-Pierre Serre became the youngest winner of the Fields Medal, at just over 28.

Homotopy Theory

1. Serre subsequently changed his research focus; he apparently thought that homotopy theory, where he had started, was already overly technical.

Theory

1. For an elementary introduction to the theory of modular forms, see Chapter VII of Jean-Pierre Serre: A Course in Arithmetic. (Web site)

Fibre

1. Using this result we deduce a similar formula for the Serre spectral sequence for a principal fibration with fibre the classifying space of a cyclic p-group. (Web site)

Finitely

1. This problem was first raised by Serre with K a field (and the modules being finitely generated). (Web site)
2. Using this bijection, he proved that every coherent subcategory of finitely presented R -modules is a Serre subcategory. (Web site)

Notion

1. This notion arises from Serre 's C-theory.

Cartan

1. Cartan, Henri; Serre, Jean-Pierre (1952a), "Espaces fibrés et groupes d’homotopie.

Homotopy Groups

1. Most modern computations use spectral sequence s, a technique first applied to homotopy groups of spheres by Jean-Pierre Serre.

Work

1. The Serre spectral sequence provided a tool to work effectively with the homology of fibrings. (Web site)

Algebraic Geometry

1. It is closely linked to algebraic geometry, especially through the work of Jean-Pierre Serre in GAGA.

Vector Bundles

1. The analogous result in algebraic geometry, due to Serre (1955, §50) applies to vector bundles in the category of affine varieties. (Web site)
2. Then, after defining the notion of a dual bundle to a complex vector bundle, the author proves a version of Serre duality for vector bundles. (Web site)
3. In turn, Jean-Pierre Serre used the analogy of vector bundles with projective modules to found in 1959 what became algebraic K-theory.

Fibration

1. A loop space is a fibre in the Serre fibration over the space (here is the path space).
2. A key turning point of the theory is that the realization of a Kan fibration is a Serre fibration of spaces.
3. A key turning point of the theorem is that the realization of a Kan fibration is a Serre fibration of spaces.

Spectral Sequence

1. The Serre spectral sequence was used by Serre to prove some of the results mentioned previously. (Web site)
2. The Serre spectral sequence relates the homology of a space to that of its loop space, so can sometimes be used to calculate the homology of loop spaces. (Web site)
3. This includes product spaces and covering spaces as special cases, and can be proven by the Serre spectral sequence on homology of a fibration.

Spectral Sequences

1. Most modern computations use spectral sequences, a technique first applied to homotopy groups of spheres by Jean-Pierre Serre.
2. Jean-Pierre Serre used spectral sequences to show that most of these groups are finite, the exceptions being π n(S n) and π 4 n −1(S 2 n).

Serre

1. For this work on spectral sequences and his work developing complex variable theory in terms of sheaves, Serre was awarded a Fields Medal in 1954. (Web site)
2. Serre uses spectral sequences to the study of the relations between the homology groups of fibre, total space and base space in a fibration. (Web site)
3. Serre introduced Cech cohomology of sheaves in this paper, and, despite its technical deficiencies, revolutionized algebraic geometry.

Categories

1. Spectral Sequences
2. Mathematics > Topology > Algebraic Topology > Fibration
3. Sheaves
4. Science > Mathematics > Geometry > Algebraic Geometry
5. Vector Bundles
6. Books about "Serre" in Amazon.com
   

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