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ARTICLES RELATED TO Serre

Serre: Encyclopedia - Coherent sheaf

In mathematics, especially in algebraic geometry and the theory of complex manifolds, a coherent sheaf F on a locally ringed space X is a sheaf isomorphic with the cokernel of a morphism of OX-modules OXm → OXn. Here OX is the structure sheaf of local rings, given by definition on X. The form of the definition is a global (on X) way of carrying across the idea of a finitely-presented mo ...

Including:

Coherent sheaf - Coherent cohomology

Serre: Encyclopedia - Weil conjectures

In mathematics, the Weil conjectures, which had become theorems by 1974, were some highly-influential proposals from the late 1940s by André Weil on the generating functions (known as local zeta-functions) derived from counting the number of points on algebraic varieties over finite fields. The main burden was that such zeta-functions should be rational functions, should satisfy a form of functional equation, and should have their zeroes in restricted places. The last two parts were quite consciously modelled on the Riemann zeta func ...

Including:

Weil conjectures - Background and history

Weil conjectures - Statement of the Weil conjectures

Weil conjectures - Examples

Weil conjectures - The projective line

Weil conjectures - Projective space

Weil conjectures - Elliptic curves

Weil conjectures - Weil cohomology

Serre: Encyclopedia - Arithmetic

Arithmetic or arithmetics (from the Greek word αριθμός = number) in common usage is a branch of (or the forerunner of) mathematics which records elementary properties of certain operations on numerals, though professional mathematicians often treat arithmetic as a synonym for number theory. It is the oldest and simplest branch of mathematics, used widely by almost everyone from simple daily counting to more advanced science and business. Arithmetic - Arithmetic operations.

Including:

Arithmetic - Arithmetic operations

Arithmetic - Number theory

Arithmetic - Pronunciation

Serre: Encyclopedia - Algebraic variety

In mathematics, an algebraic variety is essentially a set of common zeroes of a set of polynomials. Algebraic varieties are one of the central objects of study in classical (and to some extent, modern) algebraic geometry. Historically, the fundamental theorem of algebra established a link between algebra and geometry by saying that a polynomial in one variable over the complex numbers is determined by the set of its roots, which is an inherently geometric object. Building on this result, Hilbert's Nullstellensatz provides a fun ...

Including:

Algebraic variety - Formal definitions

Algebraic variety - Affine varieties

Algebraic variety - Projective varieties

Algebraic variety - Basic results

Algebraic variety - Discussion and generalizations

Serre: Encyclopedia II - Serge Lang - Mathematical work

He was a student of Emil Artin at Princeton University. His thesis was on quasi-algebraic closure. He then worked on the geometric analogues of class field theory and diophantine geometry. Later he moved into diophantine approximation and transcendence theory. A break in research while he was involved in trying to meet 1960s student activism half way caused him (on his own description) difficulties in picking up the threads. He wrote on modular forms and modular units, the idea of a 'distribution' on a ...

Serre: Encyclopedia II - Daniel Quillen - Biography

Quillen was born in Orange, New Jersey. He entered Harvard University, where he earned both his BA (1961) and his PhD (1964), the latter of which was completed under the supervision of Raoul Bott with a thesis in partial differential equations. Quillen obtained a position at the Massachusetts Institute of Technology after completing his doctorate. However, he also spent a number of years at several other universities. This experience would prove to be important in influencing the direction of his research. He visited France twice: fir ...

Serre

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