On the Goncharov depth conjecture and polylogarithms of depth two.

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 Li n - d + 1 , 1 , ⋯ , 1 (a 1 , a 2 , ⋯ , a d) , and we prove this latter statement for d = 2 . [ABSTRACT FROM AUTHOR]