Bogdan Zavyalov (Institute of Advanced Studies, Princeton)

Abstract: Let X be a smooth and proper variety over a local field K. Then the etale  cohomology groups H^i(X_C, Q_ell) admit the natural weight and monodromy filtrations. The weight-monodromy conjecture predicts that these two filtrations coincide up to a shift.

Recently, P. Scholze proved this conjecture for set-theoretic complete intersections
inside the projective space using the theory of perfectoid spaces.

Alternatively, one can formulate a (local) version of the weight-monodromy
conjecture for the nearby cycles. We will give a precise formulation of this
conjecture and prove it in some cases following the strategy of Scholze in the global case.

Joint work with David Hansen.

Zoom (Meeting-ID: 635 7328 0984, Password: smallest six digit prime)