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Arithmetic Geometry, Number Theory, and Computation

✍ Scribed by Jennifer S. Balakrishnan (editor), Noam Elkies (editor), Brendan Hassett (editor), Bjorn Poonen (editor), Andrew V. Sutherland (editor), John Voight (editor)

Publisher
Springer International Publishing
Year
2022
Tongue
English
Leaves
597
Series
Simons Symposia
Edition
1
Category
Library
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✦ Synopsis

This volume contains articles related to the work of the Simons Collaboration “Arithmetic Geometry, Number Theory, and Computation.” The papers present mathematical results and algorithms necessary for the development of large-scale databases like the L-functions and Modular Forms Database (LMFDB). The authors aim to develop systematic tools for analyzing Diophantine properties of curves, surfaces, and abelian varieties over number fields and finite fields. The articles also explore examples important for future research.

Specific topics include
● algebraic varieties over finite fields
● the Chabauty-Coleman method
● modular forms
● rational points on curves of small genus
● S-unit equations and integral points.

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