Search

Summary

Chapter 1 is a gentle introduction of the Mordell conjecture for beginners ofDiophantine geometry. We explain what the Mordell conjecture is, its brief history and its importance in current mathematics.

The Mordell conjecture (Faltings's theorem) is one of the most important achievements in Diophantine geometry, stating that an algebraic curve of genus at least two has only finitely many rational points. This book provides a self-contained and detailed proof of the Mordell conjecture following the papers of Bombieri and Vojta. Also acting as a concise introduction to Diophantine geometry, the text starts from basics of algebraic number theory, touches on several important theorems and techniques (including the theory of heights, the Mordell–Weil theorem, Siegel's lemma and Roth's lemma) from Diophantine geometry, and culminates in the proof of the Mordell conjecture. Based on the authors' own teaching experience, it will be of great value to advanced undergraduate and graduate students in algebraic geometry and number theory, as well as researchers interested in Diophantine geometry as a whole.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

1 - What Is the Mordell Conjecture (Faltings’s Theorem)?

Summary

The Mordell Conjecture

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

1 - What Is the Mordell Conjecture (Faltings’s Theorem)?

Summary

The Mordell Conjecture