I report on joint work with Luca Migliorini at Bologna. If you have a
map of complex projective manifolds, then the rational cohomology of the
domain splits into a direct sum of pieces in a way dictated by the
singularities of the map. By Poincaré duality, the corresponding
projections can be viewed as cohomology classes (projectors) on the
self-product of the domain. These projectors are Hodge classes, i.e.
rational and of type (p,p) for the Hodge decomposition. Take the same
situation after application of an automorphism of the ground field of
complex numbers. The new projectors are of course Hodge classes. On the
other hand, you can also transplant, using the field automorphism, the
old projectors into the new situation and it is not clear that the new
projectors and the transplants of the old projectors coincide. We prove
they do, thus proving that the projectors are absolute Hodge classes,
i.e. their being of Hodge type survives the totally discontinuous
process of a field automorphism. We also prove that these projectors
are motivated in the sense of Andre. ## Talk:Download video. |

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