Brauer–Manin obstructions on degree 2 K3 surfaces

Argentin, P.: Sur certaines surfaces de Kummer. PhD thesis, Université de Genève (2006)

Balestrieri, F., Berg, F., Manes, M., Park, J., Viray, B.: Insufficiency of the Brauer–Manin obstruction for rational points on Enriques surfaces. In: Eischen, E.E., Long, L., Pries, R., Stange, K.E. (eds.), Directions in Number Theory: Proceedings of the 2014 WIN3 Workshop, pp. 1–31. Springer International Publishing (2016)

Barth, W.P., Hulek, K., Peters, C.A.M., Van de Ven, A.: Compact Complex Surfaces, 2 edn. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 4. Springer, Berlin (2004)

Bosma, W., Cannon, J., Playoustm, C.: The Magma algebra system. I. The user language. J. Symb. Comput. 24(3-4), 235–265 (1997). Computational algebra and number theory (London, 1993)

Bright, M.: Computations on diagonal quartic surfaces. PhD thesis, Cambridge University (2002)

Colliot-Thélène, J.-L.: Points rationnels sur les fibrations. In Böröczky, K., Kollár, J., Szamuely, T. (eds.), Higher dimensional varieties and rational points: proceedings of the 2001 Budapest conference. Springer, Berlin (2003)

Colliot-Thélène, J.-L., Kanevsky, D., Sansuc, J.-J.: Arithmétique des surfaces cubiques diagonales. In: Diophantine Approximation and Transcendence Theory: Seminar, Bonn 1985. Lecture notes in mathematics, vol. 1290, pp. 1–108. Springer, Berlin (1987)

Colliot-Thélène, J.-L., Pál, A., Skorobogatov, A.N.: Pathologies of the Brauer–Manin obstruction. Math. Z. 282(3), 799–817 (2016)

Corn, P.: Del Pezzo surfaces and the Brauer-Manin obstruction. PhD thesis, University of California, Berkeley (2005)

Corn, P.: The Brauer–Manin obstruction on Del Pezzo surfaces of degree 2. Proc. London Math. Soc. 95(3), 735–777 (2007)

Corn, P.: Tate-Shafarevich groups and K3 surfaces. Math. Comput. 79, 563–581 (2010)

Festi, D.: Topics in the arithmetic of del Pezzo and K3 surfaces. PhD thesis, Leiden University (2016)

Hassett, B., Várilly-Alavarado, A.: Failure of the Hasse principle on general K3 surfaces. J. l’Inst. Math. Jussieu 12, 853–877 (2013)

Hassett, B., Várilly-Alvarado, A., Varilly, P.: Transcendental obstructions to weak approximation on general K3 surfaces. Adv. Math. 228(3), 1377–1404 (2011)

Huybrechts, D.: Lectures on K3 Surfaces. Cambridge University press, New York (2016)

Ieronymou, E., Skorobogatov, A.: Odd order Brauer–Manin obstruction on diagonal quartic surfaces. Adv. Math 270, 181–205 (2015)

Ieronymou, E., Skorobogatov, A.N., Zarhin, Y.G.: On the Brauer group of diagonal quartic surfaces. J. Lond. Math. Soc. 83(2), 659–672 (2011)

Logan, A.: The Brauer-Manin obstruction on del Pezzo surfaces of degree 2 branched along a plane section of a Kummer surface. Math. Proc. Camb. Phil. Soc. 144(3), 603–622 (2008)

Logan, A., van Luijk, R.: Nontrivial elements of Sha explained through K3 surfaces. Math. Comput. 78, 441–483 (2009)

McKinnie, K., Sawon, J., Tanimoto, S., Várilly-Alvarado, T.: Brauer Groups on K3 Surfaces and Arithmetic Applications, vol. 320, pp. 177–218. Springer, Cham (2017)

Nikulin, V.V.: Integral symmetric bilinear forms and some of their applications. Math. USSR-Izvestiya 14(1), 103 (1980)

Poonen, B.: Insufficiency of the Brauer-Manin obstruction applied to étale covers. Ann. Math. 171(3), 2157–2169 (2010)

Serre, J.-P.: Linear Representations of Finite Groups. Springer, Berlin (1977)

Serre, J.-P.: Local Fields. Springer, New York (1979). Translated from the French by Marvin Jay Greenberg

Skorobogatov, A.: Beyond the Manin obstruction. Invent. Math. 135(2), 399–424 (1999)

Skorobogatov, A.: Torsors and Rational Points. Cambridge Tracts in Mathematics, vol. 144. Cambridge University Press, Cambridge (2001)

Skorobogatov, A.: Diagonal quartic surfaces. Oberwolfach Rep. 33, 76–79 (2017)

Skorobogatov, A.N., Zarhin, Y.G.: Kummer varieties and their Brauer groups. arXiv:1612.05993 (2016)

Smeets, A.: Insufficiency of the étale Brauer–Manin obstruction: towards a simply connected example. Am. J. Math. 139(2), 417–431 (2017)

Várilly-Alvarado, A.: Weak approximation on del Pezzo surfaces of degree 1. Adv. Math. 219(6), 2123–2145 (2008)

Várilly-Alvarado, A.: Arithmetic of K3 surfaces. In: Bogomolov, F., Hassett, B., Tschinkel, Y. (eds.), Geometry Over Nonclosed Fields, vol. 5, pp. 197–248. Springer, Berlin (2017)

Yuri, I.: Manin. Le groupe de Brauer-Grothendieck en géométrie diophantienne. Actes due Congrés International des Mathématiciens (Nice. 1970), Tome 1, pp. 401–411. Gauthier-Villars, Paris (1971)