Rational points over C1 fields

TL;DR

This paper discusses Manin's 1966 conjecture on rational points over C1 fields, reviewing its formulation and subsequent developments in the context of rational surfaces over perfect fields.

Contribution

It provides a concise overview of Manin's conjecture and summarizes key developments related to rational points over C1 fields.

Findings

Manin's conjecture remains influential in the study of rational points.

Progress has been made in understanding rational surfaces over perfect fields.

The note highlights ongoing research directions and unresolved questions.

Abstract

This is a small note on Manin's 1966 article on rational surfaces over perfect fields, the conjecture he formulates there, and later developments. This text is by no means exhaustive and reflects the author's understanding and interest. References for background and general studies are provided.