I will discuss a conjecture of A. Kuzntesov and E. Shinder that asserts that the difference [X]-[Y] of the classes of two algebraic varieties whose derived categories of coherent sheaves are equivalent must be annihilated by some power of the class of the affine line. I will explain two examples involving K3 surfaces of degree 8 and 12 where this conjecture has been verified.
Speaker(s): Igor Dolgachev (UM)