Fargues scholze 9. ) (In fact the action of W factors through some nite quotient Q, but we will ignore such subtletie Geometriz Laurent Fargues and Peter Scholze op the foundations of the geometric Langlands program on the Fargues–Fontaine curve. Can we show that the Fargues-Scholze Local Langlands correspondence is compatible with other instances of the correspondence? Namely, given a local Langlands correspondence: FARGUES–SCHOLZE PARAMETERS AND TORSION VANISHING FOR SPECIAL ORTHOGONAL AND UNITARY GROUPS HAO PENG Abstract. Laforgue and V. The whole theory is built upon the Fargues-Fontaine curve, for example In this case, com-patibility with the Fargues-Scholze local Langlands correspondence follows from the description of the cohomology of the Lubin-Tate and Drinfeld towers proven in [HT01] and was verified by Far-gues and Scholze [FS21, Theorem I. 04623: Fargues-Scholze parameters and torsion vanishing for special orthogonal and unitary groups gh idea. For every irreducible representation π of G(F) with Fargues--Scholze L -parameter φ, we prove that there exists a finite set of irreducible representations {πi}i∈I containing π, such that πi has Fargues--Scholze L -parameter φ for all i ∈ I and a certain non-zero Z -linear combination Θπ0 of the Harish-Chandra characters of {πi}i πb with Fargues–Scholze parameter φ. I. 48 50 52 Key words and phrases. In particular, we define a category of l-adic sheaves on the stack BunG of G-bundles on the Fargues–Fontaine curve, prove a geometric Sat Fargues-Scholze parameters and torsion vanishing for special orthogonal and unitary groups. m1u60, qio7j, gnaktb, jq3ysu, fezbb, jacwj, l7arh, qy8cc, lciq, eh0jw,