Resumen de On the Goncharov depth conjecture and polylogarithms of depth two

Steven Charlton, Herbert Gangl, Danylo Radchenko, Daniil Rudenko

• We prove the surjectivity part of Goncharov’s depth conjecture over a quadratically closed field. We also show that the depth conjecture implies that multiple polylogarithms of depth d and weight n can be expressed via a single function Lin−d+1,1,...,1(a1, a2,..., ad ), and we prove this latter statement for d = 2