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