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Frobenius modules appear in the Riemann Hilbert correspondence.

Frobenius algebras appear in TQFT.

Is there a way to pass from one to the other?

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  • $\begingroup$ Could you please include basic definitions such as Frobenius modules and Frobenius algebras? I also don't understand how Frobenius modules appear in the Riemann–Hilbert correspondence unless in char p. $\endgroup$
    – Z. M
    Commented Dec 19, 2022 at 17:41
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    $\begingroup$ IIRC the "Frobenius modules" which appear in Riemann-Hilbert appear in Riemann-Hilbert over $\mathbb F_p$, and are so-named because of their relation to the Frobenius endomorphism $x \mapsto x^p$. Whereas the "Frobenius algebras" appearing in TQFT are usually studied in characteristic 0, and don't really have anything to do with a choice of prime or the map $x \mapsto x^p$. So I'm pretty sure this is just a case of multiple things being named after the same person. $\endgroup$
    – Tim Campion
    Commented Dec 19, 2022 at 17:47

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