Algebraic Geometry Seminar

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Ngo's support theorem and Lagrangian fibrations

Speaker: Christian Schnell, Stony Brook University

Location: Warren Weaver Hall 512

Date: Tuesday, March 18, 2025, 5 p.m.

Synopsis:

In 2010, Ngo proved the "fundamental lemma". A key step in his proof is the "support theorem". This is a result about abelian fibrations (= families of abelian varieties with singular fibers); it describes the perverse sheaves that appear in the decomposition of the direct image of the constant sheaf. Ngo's proof uses reduction to finite fields. I will present a new proof that only uses complex geometry (and that works in the Kaehler case); and then discuss applications to Lagrangian fibrations on holomorphic symplectic manifolds.