A Jacobian criterion for artin v-stacks

• Linus Hamann ^[1]
  1. [1] Harvard University

     Harvard University

     City of Cambridge, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 32, Nº. 2, 2026
• Idioma: inglés
• DOI: 10.1007/s00029-026-01139-9
• Enlaces
  • Texto completo
• Resumen

  • We prove a generalization of the Jacobian criterion of Fargues-Scholze for spaces of sections of a scheme smooth quasi-projective over the algebraic Fargues-Fontaine curve [8, Section IV.4]. Namely, we show how to use their criterion to deduce an analogue for spaces of sections of a smooth Artin stack over the algebraic curve obtained by taking the stack quotient of such a relatively smooth quasi-projective scheme by the action of a linear algebraic group. As an application, we show various moduli stacks appearing in the Fargues-Scholze geometric Langlands program are cohomologically smooth Artin v-stacks and compute their l -dimensions.

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