Arakelov theory information

In mathematics, Arakelov theory (or Arakelov geometry) is an approach to Diophantine geometry, named for Suren Arakelov. It is used to study Diophantine...

mathematician of Armenian descent known for developing Arakelov theory. From 1965 onwards Arakelov attended the Mathematics department of Moscow State University...

has also worked in Hodge–Arakelov theory and p-adic Teichmüller theory. Mochizuki developed inter-universal Teichmüller theory, which has attracted attention...

Approximation theory — Arakelov theory — Asymptotic theory — Bifurcation theory — Catastrophe theory — Category theory — Chaos theory — Choquet theory — Coding...

compact. Potential theory Serre duality Helmholtz decomposition Local invariant cycle theorem Arakelov theory Hodge-Arakelov theory ddbar lemma, a key...

the application. In category theory, 1 is the terminal object of a category if there is a unique morphism. In number theory, 1 is the value of Legendre's...

theories. Almgren–Pitts min-max theory Approximation theory Arakelov theory Artin–Schreier theory Asymptotic theory Automata theory Bass–Serre theory...

geometry. In the 1970s, Suren Arakelov developed Arakelov heights in Arakelov theory. In 1983, Faltings developed his theory of Faltings heights in his proof...

elements. Also in set theory, 0 is the lowest ordinal number, corresponding to the empty set viewed as a well-ordered set. In order theory (and especially its...

fields and the usual metric on the non-Archimedean fields. Arakelov theory Arakelov theory is an approach to arithmetic geometry that explicitly includes...

of Arakelov geometry were realized in this setup. He holds the position of senior research fellow at the Laboratory of Algebra and Number Theory at the...

= 0. The theory consists both of theorems and many conjectures and open questions. Glossary of arithmetic and Diophantine geometry Arakelov geometry Hindry...

amongst other desirable ones. A full resolution is given by Arakelov theory. Arakelov theory offers a solution to the problem presented above. Intuitively...

application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study...

polynomials or trigonometric polynomials) Arakelov geometry also known as Arakelov theory Arakelov theory an approach to Diophantine geometry used to...

ISBN 0-387-96447-9. MR 0886677. Lang, Serge (1988). Introduction to Arakelov theory. New York: Springer-Verlag. doi:10.1007/978-1-4612-1031-3. ISBN 0-387-96793-1...

Szpiro, with the thesis Théorie d'Arakelov et courbes modulaires on Arakelov theory and modular curves. At Paris-Sud, Michel Raynaud was one of his mentors...

develop parallel techniques on the number field side. The development of Arakelov theory and its exploitation by Gerd Faltings in his proof of the Mordell conjecture...

development by Jean-Benoît Bost removed this problem with the use of Arakelov theory, and research in this area is ongoing. The example below gives an idea...

Medicine Positron emission tomography (PET) (1974) Suren Arakelov Soviet Union Mathematics Arakelov theory (1974) Raymond Damadian United States Medicine Magnetic...