A Survey of the Hodge|Arakelov Theory of Elliptic Curves I

A Survey of the Hodge-Arakelov Theory of Elliptic Curves I

[Mzk1,2]) — i.e., a sort of “Hodge theory of elliptic curves” analogous to the classical complex and p-adic Hodge theories, but which exists in the global ...

A Survey of the Hodge-Arakelov Theory of Elliptic Curves II

Keywords: elliptic curve, universal extension, Kodaira-Spencer mor- phism, Hodge Theory, crystalline, theta function, Galois action, Frobenius morphism, ...

The Hodge-Arakelov Theory of Elliptic Curves : Global Discretization ...

The purpose of this paper is to study the Hodge-Arakelov theory of elliptic curves (cf. [Mzk1-4]) in positive characteristic.

The Hodge-Arakelov Theory of Elliptic Curves - RIMS, Kyoto University

... survey various examples of Arakelov-theoretic torsors that arise naturally in arithmetic geometry. For a more detailed discussion of the ideas surrounding ...

A Survey of the Hodge-Arakelov Theory of Elliptic Curves II

This theory is a sort of "Hodge theory of elliptic curves" analogous to the classical complex and p p -adic Hodge theories, but which exists in the global ...

Hodge–Arakelov theory - Wikipedia

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

A Survey of the Hodge-Arakelov Theory of Elliptic Curves II

The purpose of the present manuscript is to give a survey of the Hodge-Arakelov theory of elliptic curves (cf. [Mzk1,2]) — i.e., a sort of “Hodge theory of ...

A survey of the Hodge-Arakelov theory of elliptic curves. II

... a survey of the Hodge-Arakelov theory of elliptic curves [cf. S. Mochizuki, Global discretization of local Hodge theories, RIMS Preprint Nos. 1255, 1256 ...

A Survey of The Hodge-Arakelov Theory of Elliptic Curves II | PDF ...

This document summarizes recent developments in the Hodge-Arakelov theory of elliptic curves. It begins by reviewing how the classical Kodaira-Spencer ...

Introduction to Hodge Theory via the example of Elliptic Curves

In the. 1930s, British mathematician William Vallance Douglas Hodge started enriching the theories about de Rham cohomology to study algebraic ...

[math/0312359] On the Arakelov theory of elliptic curves - arXiv

This note contains an elementary discussion of the Arakelov intersection theory of elliptic curves. The main new results are a projection formula for elliptic ...

Philosophy behind Mochizuki's work on the ABC conjecture

... A survey of the Hodge-Arakelov Theory of Elliptic Curves I". Mochizuki is an extremely good writer!! If you elide unclear technical issues ...

Anabelian Geometry in the Hodge-Arakelov Theory of Elliptic ...

... a survey of the Hodge-Arakelov theory of elliptic curves [cf. S. Mochizuki, Global discretization of local Hodge theories, RIMS Preprint Nos.

Shinichi Mochizuki - A Survey of the Hodge-Arakelov Theory of ...

A Survey of the Hodge-Arakelov Theory of Elliptic Curves II. Algebraic Geometry 2000. Azumino, Adv. Stud. Pure Math. 36, Math. Soc. Japan. S. Mochizuki. Volume ...

A road to inter-universal Teichmuller theory - MathOverflow

A Survey of the Hodge-Arakelov Theory of Elliptic Curves II. Particularly interesting is Fesenko's recent extended remarks on IUT (and learning ...

arXiv:math/0312359v2 [math.NT] 6 Sep 2004

This note contains an elementary discussion of the Arakelov intersection theory of elliptic curves. The main new results are a projection formula for elliptic.

EXPLICIT ARAKELOV GEOMETRY - math.leidenuniv.nl

In Chapter 5, where we study the Arakelov theory of elliptic curves more closely, we give an alternative proof of Corollary 2.3.2. This proof relies on ...

Hodge theory of p-adic varieties: a survey - IMJ-PRG

(2) 1967–70: Tate and Grothendieck discover that, for an elliptic curve over. K (or, more generally, an abelian variety), its de Rham cohomology and its p-adic ...

Shimura curves and the abc conjecture - ScienceDirect.com

Let E be an elliptic curve over Q . By the modularity theorem [110], [100], [10] there is a non-constant modular parametrization ...

A Survey of Elliptic Cohomology in nLab

Hodge theory, Hodge theorem · nonabelian Hodge theory ... Hence the assignment of cohomology theories to elliptic curves is ...