Shankar–Tsimerman's Jacobian isogeny conjecture for abelian fourfolds

Let pp be a prime, let AA be a 44-dimensional abelian variety over Fp\overline{\mathbf{F}}_p, and let a stable curve be allowed to be possibly reducible. Shankar–Tsimerman's conjecture. The variety AA is isogenous to the Jacobian of some stable curve.

This conjecture asks whether every abelian fourfold over an algebraic closure of a finite field lies, up to isogeny, in the Jacobian locus after allowing stable reducible curves. The source attributes it to Shankar–Tsimerman and does not state that it has been resolved.

Sources & referencesView supporting material

Primary source

Taylor Dupuy, Kiran Kedlaya, David Roe and Christelle Vincent, “Isogeny Classes of Abelian Varieties over Finite Fields in the LMFDB”, arXiv:2003.05380 (2020).

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