Related papers: An Introduction to Mordell Weil Theorem

We provide a new approach to studying the moduli space of curves via Morse theory and hyperbolic geometry, by introducing a family of Morse functions on the moduli space $\overline{\mathcal{M}}_{g,n}$ of stable curves of genus $g$ with $n$…

This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.

In this paper, firstly the axis of a slant helix is found with a method. Secondly, the theorem which characterizes a unit speed curve to be a slant helix is proved in detail. The importance of this theorem is stemed from that it has led to…

This paper is a survey on Deduction modulo theory

The purpose of this book is to build up the fundament of an Arakelov theory over adelic curves in order to provide a unified framework for the researches of arithmetic geometry in several directions.

Expanded lecture notes. Preliminary version, comments are welcome.

This is a hands on introduction to McMullen's Polytope Algebra. More than interesting on its own, this algebra was McMullen's tool to give a combinatorial proof of the g-theorem.

Foundational cases of the generalized Stokes' theorem are visualized using geometric algebra. From considering bivector valued fields, two seldom used instances of the theorem are obtained. Graphical representations are given, showing a…

In this paper we discuss a general notion of Weil cohomology theories, both in algebraic geometry and in rigid analytic geometry. We allow our Weil cohomology theories to have coefficients in arbitrary commutative ring spectra. Using the…

Given a non-isotrivial elliptic curve over $\mathbb{Q}(t)$ with large Mordell-Weil rank, we explain how one can build, for suitable small primes $p$, infinitely many fields of degree $p^2-1$ whose ideal class group has a large $p$-torsion…

This text provides an introduction and complements to some basic constructions and results in 2-representation theory of Kac-Moody algebras.

Let $E$ be an elliptic curve over a number field $K$. Descent calculations on $E$ can be used to find upper bounds for the rank of the Mordell-Weil group, and to compute covering curves that assist in the search for generators of this…

This is an elementary exposition of the basic descent theorems for algebraic schemes over fields (Grothendieck, Weil, ...).

Torelli's theorem is proven by the study of the convolution product of the intersection cohomology sheaf of the thetadivisor.

A tutorial introduction into the principles of Orbital Physics in strongly correlated transition metal oxides.

We introduce the tautological rings of moduli stacks of twisted curves and establish some basic properties.

We define Strebel differentials for stable complex curves, prove the existence and uniqueness theorem that generalizes Strebel's theorem for smooth curves, prove that Strebel differentials form a continuous family over the moduli space of…

We prove a second main theorem for elliptic projective planes.

We introduce the Frenet theory of curves in dual space $\d^3$. After defining the curvature and the torsion of a curve, we classify all curves in dual plane with constant curvature. We also establish the fundamental theorem of existence in…

We formulate a refined theory of linear systems, using the methods of a previous paper, "A Theory of Branches for Algebraic Curves", and use it to give a geometric interpretation of the genus of an algebraic curve. Using principles of…