Une conjecture $C_{\rm st}$ pour la cohomologie \`a support compact
Pierre Colmez, Sally Gilles, Wies{\l}awa Nizio{\l}

TL;DR
The paper proves that certain p-adic functions eliminate higher-degree Galois cohomology on the Fargues-Fontaine curve, enabling new conjectures for p-adic analytic varieties' cohomology with compact support.
Contribution
It introduces p-adic analogs of logarithmic functions that trivialize Galois cohomology, facilitating the formulation of $C_{dR}$ and $C_{st}$ conjectures for compact support cohomology.
Findings
Adding p-adic logs kills Galois cohomology in degrees ≥ 1.
Results are analogous to folklore for $f B^+_{dR}$.
Enables new conjectures for p-adic analytic varieties' cohomology.
Abstract
Let be the ring of analytic functions on the Fargues-Fontaine curve . We show that adding -adic analogs of and kills its Galois cohomology in degrees~. The analogous result for is folklore. This makes it possible to formulate and -type conjectures for compact support cohomology of -adic analytic varieties.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Meromorphic and Entire Functions
