Mathematical analysis demonstrates the construction of algebraic cycles for Hodge classes, highlighting algebraicity via Borcherds products and G-functions.
We construct the algebraic cycle attached to a Hodge class. For divisor Hodge loci we use Borcherds products where the Frobenius unit satisfies u=1. In general we use integrality, Kedlaya unit-root extension, Crew, Fontaine-Laffaille, rigid maximum principle and norm descent to obtain ord_D(u)=0. Combined with pλ=λ⇒λ=0 and weight rigidity this yields flatness and algebraicity via G-functions.
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Jean Florent Romaric GNAYORO (2026) studied this question.
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