In this thesis, rational points on K3 surfaces are studied. In the first part of Chapter 1 the Brauer group and the the Brauer-Manin obstruction are introduced. The second part of Chapter 1 is... Show moreIn this thesis, rational points on K3 surfaces are studied. In the first part of Chapter 1 the Brauer group and the the Brauer-Manin obstruction are introduced. The second part of Chapter 1 is devoted to the introduction of the refined Swan conductor and the link between the latter and the Brauer-Manin set. The aim of Chapter 2 is to give the first example of a K3 surface over a number field (in fact, over the rational numbers) for which a prime of good reduction is involved in the Brauer-Manin obstruction; this gives a negative answer to a question originally asked by Swinnerton-Dyer. In Chapter 3 the role of primes of good reduction in the Brauer-Manin obstruction is discussed, with a focus on K3 surfaces. Finally, in the last chapter, after introducing some techniques that can be used to compute the refined Swan conductor, several examples of Brauer-Manin obstruction on K3 surfaces are provided, with a focus on Kummer K3 surfaces. Show less
