Shankar–Tsimerman's Jacobian isogeny conjecture for abelian fourfolds
Shankar–Tsimerman's Jacobian isogeny conjecture for abelian fourfolds
Let be a prime, let be a -dimensional abelian variety over , and let a stable curve be allowed to be possibly reducible. Shankar–Tsimerman's conjecture. The variety 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).
Progress summary
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