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

Hodge–Arakelov theory of elliptic curves is an analogue of classical and p-adic Hodge theory for elliptic curves carried out in the framework of Arakelov theory...

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

to 1 in many programming languages. In lambda calculus and computability theory, natural numbers are represented by Church encoding as functions, where...

Szpiro, Ullmo & Zhang 1997), he further developed his theory of 'positive line bundles' in Arakelov theory which culminated in a proof of the Bogomolov conjecture...

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

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

anabelian geometry, and the development of p-adic Teichmüller theory, Hodge–Arakelov theory and Frobenioid categories. It was developed with explicit references...

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

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

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

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

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

mathematical theories. Almgren–Pitts min-max theory Approximation theory Arakelov theory Asymptotic theory Automata theory Bass–Serre theory Bifurcation theory Braid...

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...

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...

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

Other versions of the arithmetic Riemann–Roch theorem make use of Arakelov theory to resemble the traditional Riemann–Roch theorem more exactly. The...

Anabelian geometry is a theory in number theory which describes the way in which the algebraic fundamental group G of a certain arithmetic variety X,...

section 3 Hyodo 1991 Tsuji 1999 Hodge theory Arakelov theory Hodge-Arakelov theory p-adic Teichmüller theory Tate, John (1967), "p-Divisible Groups""...

conjecture was proven by Emmanuel Ullmo and Shou-Wu Zhang in 1998 using Arakelov theory. A further generalization to general abelian varieties was also proved...

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

compact Riemannian manifold. One of the most important motivations for Arakelov theory is the zeta functions for operators with the method of heat kernels...

rings. His interests range throughout Algebraic Number Theory, Arakelov theory, Iwasawa theory, problems related to the existence and classification of...

after W. V. D. Hodge, a Scottish mathematician. Hodge algebra Hodge–Arakelov theory Hodge bundle Hodge conjecture Hodge cycle Hodge–de Rham spectral sequence...

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

obstacle to analyzing Diophantine equations with geometric tools. Arakelov theory overcomes this obstacle by compactifying affine arithmetic schemes...

of Dan Abramovich, Jean-François Burnol, and Jürg Kramer: Lectures on Arakelov Geometry. Cambridge Studies in Advanced Mathematics 33. Cambridge University...

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...