Summary
We give an account of some recent work on the existence of rational points on varieties over function fields, starting with basic material on deformation theory and the bend-and-break theorem. We emphasize the connection with the geometry of moduli spaces and include a sketch of the irreducibility of M g as a model. All details are relegated to the references.
2010 Mathematics subject classification. Primary: 14D06. Secondary: 14G05.
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Lieblich, M. (2010). Deformation Theory and Rational Points on Rationally Connected Varieties. In: Colliot-Thélène, JL., Garibaldi, S., Sujatha, R., Suresh, V. (eds) Quadratic Forms, Linear Algebraic Groups, and Cohomology. Developments in Mathematics, vol 18. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6211-9_5
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