Denis–Mordell–Lang conjecture for q-varieties and Drinfeld modules

About 12 years old · traced to

Assume that (F,Φ)(F,\Phi) is an AA-module, HotiFH ot i F is a qq-variety, and Γ=Ax1+…+Axr\Gamma=Ax_1+\ldots+Ax_r is generated by elements of FF. Define the division hull

Γ‾=xotiFoti such that ∃aot=0otiA with Φa(x)otiΓ.\overline{\Gamma}={x ot i F ot i\text{ such that }\exists a ot=0 ot i A\text{ with }\Phi_a(x) ot i\Gamma}.

Denis–Mordell–Lang conjecture. There exists an AA-module GotiHG ot i H such that

[Goti⋂Γ‾:Goti⋂H]<∞.[G ot i\bigcap\overline{\Gamma}:G ot i\bigcap H]<\infty.

The source says this conjecture implies the preceding Denis–Faltings analogue and identifies it as an analogue of the Mordell–Lang conjecture. Its resolution status is not specified.

References

Primary source

Alain Thiéry, “q-Varieties and Drinfeld Modules”, arXiv:1409.5281 (2014).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.