Saturday, December 8, 2012

Grothendieck


Who is Grothendieck?
Answer:He is the god in algebraic geometry
Alexander Grothendieck is a mathematician and the central figure behind the creation of the modern theory of algebraic geometry. His research program vastly extended the scope of the field, incorporating major elements of commutative algebra, homological algebra,sheaf theory, and category thei into its foundations. This new perspective led to revolutionary advances across many areas of pure mathematics.
Within algebraic geometry itself, his theory of schemes has become the universally accepted language for all further technical work. His generalization of the classical Riemann-Roch theorem launched the study of algebraic and topological K theory. His construction of new cohomology theories has left deep consequences for algebraic number theory,algebraic topology, and representation theory. 
One of his most celebrated achievements is the discovery of the first arithmetic Weil cohomology theory. This key result opened the way for a proof of the Weil conjectures, ultimately completed by his student Pierre. To this day, l-adic cohomology remains a fundamental tool for number theorists, with important applications to the Langlands programme.
Grothendieck’s way of thinking has influenced generations of mathematicians long after his departure from mathematics. His emphasis on the role of universal properties brought category into the mainstream as an important organizing principle. His notion of abelian category is now the basic object of study in homological algebra.
His work really has created a new page for algebraic geometry.That's why he is called the god~~

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