Une conjecture $C_{\mathrm{st}}$ pour la cohomologie à support compact

Abstract

Let $\mathbf{B}$ be the ring of analytic functions on the Fargues-Fontaine curve $Y_{\mathrm{FF}}$. We shaw that, by adding sufficiently iterated periods, one can kill its Galois cohomology in degrees $\ge 1$. For ${\mathbf{B}}_{\mathrm{dR}}^{+}$, the corresponding result is obtained by adjoining just $\log t$ and is folklore. This allows to formulate $C_{\mathrm{dR}}$ and $C_{\mathrm{st}}$ conjectures for the compactly supported cohomology of $p$-adic analytic varieties.

arXiv commentThis is a major revision: the original definition of ${\mathbf{B}}_{\mathrm{pFF}}$ ring was not correct and we present here a corrected construction