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講演タイトル
Algebraic cycles and functorial lifts from G2 to PGSp(6).
アブストラクト
We will consider the part V of the étale cohomology of the Siegel variety S of dimension 6 corresponding to a cuspidal automorphic representation of PGSp(6) which is a Langlands functorial lift from the exceptional group G2. Gross and Savin conjectured that the Galois invariant line contained in V is generated by the cohomology class of a Hilbert subvariety of S. I will explain how to reduce this global conjecture to a local statement, namely the non-vanishing of an archimedean integral. This is a joint work with Cauchi and Rodrigues Jacinto (arXiv:2202.09394).