In the 1950s Lang studied the properties of C_1 fields, that is, fields over which every homogeneous polynomial of degree at most n in n+1 variables has a nontrivial solution. Around 2000 he conjectured that smooth proper rationally connected varieties over C_1 fields have rational points. I will introduce the conjecture and show how to find points on complete intersections of forms of products of projective spaces over C_1 fields of characteristic 0.

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