Geometrization of the local Langlands correspondence

Chapter I. Introduction
	I.1. The local Langlands correspondence
	I.2. The big picture
	I.3. The Fargues–Fontaine curve
	I.4. The geometry of BunG
	I.5. -adic sheaves on BunG
	I.6. The geometric Satake equivalence
	I.7. Cohomology of moduli spaces of shtuka
	I.8. The stack of L-parameters
	I.9. Construction of L-parameters
	I.10. The spectral action
	I.11. The origin of the ideas
	I.12. Acknowledgments
	I.13. Notation
Chapter II. The Fargues–Fontaine curve and vector bundles
	II.1. The Fargues–Fontaine curve
	II.2. Vector bundles on the Fargues–Fontaine curve
	II.3. Further results on Banach–Colmez spaces
Chapter III. BunG
	III.1. Generalities
	III.2. The topological space |BunG|
	III.3. Beauville–Laszlo uniformization
	III.4. The semistable locus
	III.5. Non-semistable points
Chapter IV. Geometry of diamonds
	IV.1. Artin stacks
	IV.2. Universally locally acyclic sheaves
	IV.3. Formal smoothness
	IV.4. A Jacobian criterion
	IV.5. Partial compactly supported cohomology
	IV.6. Hyperbolic localization
	IV.7. Drinfeld\'s lemma
Chapter V. Dt(BunG)
	V.1. Classifying stacks
	V.2. Étale sheaves on strata
	V.3. Local charts
	V.4. Compact generation
	V.5. Bernstein–Zelevinsky duality
	V.6. Verdier duality
	V.7. ULA sheaves
Chapter VI. Geometric Satake
	VI.1. The Beilinson–Drinfeld Grassmannian
	VI.2. Schubert varieties
	VI.3. Semi-infinite orbits
	VI.4. Equivariant sheaves
	VI.5. Affine flag variety
	VI.6. ULA sheaves
	VI.7. Perverse Sheaves
	VI.8. Convolution
	VI.9. Fusion
	VI.10. Tannakian reconstruction
	VI.11. Identification of the dual group
	VI.12. Cartan involution
Chapter VII. D(X)
	VII.1. Solid sheaves
	VII.2. Four functors
	VII.3. Relative homology
	VII.4. Relation to Dt
	VII.5. Dualizability
	VII.6. Lisse sheaves
	VII.7. Dlis(BunG)
Chapter VIII. L-parameter
	VIII.1. The stack of L-parameters
	VIII.2. The singularities of the moduli space
	VIII.3. The coarse moduli space
	VIII.4. Excursion operators
	VIII.5. Modular representation theory
Chapter IX. The Hecke action
	IX.1. Condensed -categories
	IX.2. Hecke operators
	IX.3. Cohomology of local Shimura varieties
	IX.4. L-parameter
	IX.5. The Bernstein center
	IX.6. Properties of the correspondence
	IX.7. Applications to representations of G(E)
Chapter X. The spectral action
	X.1. Rational coefficients
	X.2. Elliptic parameters
	X.3. Integral coefficients
Bibliography