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). We 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 pointsThis proceedings volume contains articles related to the research presented at the 2020 Workshop on Arithmetic Geometry, Number Theory, and Computation. The authors' common perspective is that advances in computational techniques accelerate research in arithmetic geometry and number theory, as a source of both data and examples, and as an impetus for effective results. The dynamic interplay between experiment, theory, and computation has historically played a pivotal role in the development of number theory. In the 18th and 19th centuries, Euler and Gauss undertook extensive calculations by hand in the pursuit of data to help formulate and refine conjectures, and as a source of counterexamples. In the 20th century, systematic computations of elliptic curves and their L-functions led to the formulation of the Sato-Tate and modularity conjectures, both of which have now been proved, and the conjecture of Birch and Swinnerton-Dyer, which remains open but has been proved in some special cases.In the 21st century, the frontier of research in arithmetic geometry has moved on to curves of higher genus, abelian varieties, and K3 surfaces. Although available computational resources have grown dramatically, the development and implementation of practical algorithms has lagged behind the theory; the present volume is a step towards correcting this imbalance. In contrast to the situation with elliptic curves, in higher dimensions brute-force computation yields very little. To obtain practical algorithms, one must exploit the theoretical infrastructure of modern arithmetic geometry.weiterlesen