# Meeting Details

Title: Hodge groups of certain superelliptic jacobians (joint work with Jiangwei Xue) Algebra and Number Theory Seminar Yuri Zarhin, Penn State Hodge groups (aka special Mumford--Tate groups) of complex abelian varieties were introduced in 1960s by David Mumford and John Tate. While abelian varieties are complex projective algebraic varieties, their Hodge groups are reductive linear algebraic groups over the rationals. The tensor invariants of the Hodge group are exactly the Hodge classes on self-products of the abelian variety involved. In other words, one may restate the celebrated Hodge conjecture as an assertion about the algebraicity of tensor invariants of Hodge groups. In this talk we discuss explicit computations of Hodge groups for a certain class of superelliptic jacobians. It turns out that for this class the Hodge groups are as large as possible".