the fargues-fontaine curve associated to an algebraically closed nonarchimedean field of characteristic $p$ is a fundamental geometric object in $p$-adic hodge theory. via the tilting equivalence it is related to the galois theory of finite extensions of q_p; it also occurs in fargues's program to geometrize the local langlands correspondence for such fields.

recently, peter dillery and alex youcis have proposed using a related object, the "affine cone" over the aforementioned curve, to incorporate some recent insights of kaletha into fargues's program. i will summarize what we do and do not yet know, particularly about vector bundles on this and some related spaces (all joint work in progress with dillery and youcis).