Zarhin's trick and geometric boundedness results for K3 surfaces

Zarhin's trick and geometric boundedness results for K3 surfaces

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François Charles , Université Paris-Sud
IAS Room S-101

Please note special time.  Tate's conjecture for divisors on algebraic varieties can be rephrased as a finiteness statement for certain families of polarized varieties with unbounded degrees. In the case of abelian varieties, the geometric part of these finiteness statements is contained in Zarhin's trick. We will discuss such geometric boundedness statements for K3 surfaces over arbitrary fields and holomorphic symplectic varieties, with application to direct proofs of the Tate conjecture for K3 surfaces that do not involve the Kuga-Satake correspondence.