Gaitsgory, DennisNam, Taeuk2026-07-0720262026-05-082026Nam, Taeuk. 2026. Towards a Tamely Ramified Geometric Langlands Correspondence. Doctoral Dissertation, Harvard University Graduate School of Arts and Sciences.32674850https://dash.harvard.edu/handle/1/42744142Motivated by the recent proof of the unramified global geometric Langlands correspondence, we make progress towards constructing a tamely ramified version of the global geometric Langlands correspondence. We show that the DG category of D-modules on the moduli stack of principal G-bundles on a smooth, projective, connected curve with Iwahori level structure at a point is compactly generated, which allows the Langlands functor to be constructed in this setting. We then study the local behaviour of this correspondence by constructing factorization module categories at a point and constructing equivalences between them. These equivalences are factorization module categorical versions of the Arkhipov-Bezrukavnikov equivalence, Bezrukavnikov’s equivalence, and an Iwahori invariant Fundamental Local Equivalence.application/pdfenCompact GenerationFundamental Local EquivalenceGeometric LanglandsIwahoriModuli StackTame RamificationMathematicsTheoretical mathematicsThesis or Dissertation2026-07-070000-0002-8135-3232