- Compactification and Derived
Representations{#toc-compactification-and-derived-representations}
- Fixed Points and Invariants{#toc-fixed-points-and-invariants}
- Linearization and Matrix Representations with Lie Groups{#toc-linearization-and-matrix-representations-with-lie-groups}
- Abelianization and Completions{#toc-abelianization-and-completions}
- Sieves, Filtrations, Spectral Sequences{#toc-sieves-filtrations-spectral-sequences}
- Projections, Ramifications, and Cohomology{#toc-projections-ramifications-and-cohomology}
- Extensions, Closures, and Automorphisms{#toc-extensions-closures-and-automorphisms}
- Quotients and Reductions{#toc-quotients-and-reductions}
- Diffusion, Gaussian Isotropy Group, Skeleton Category{#toc-diffusion-gaussian-isotropy-group-skeleton-category}
- Inverse Limits, Profinite Groups, Absolute Galois Groups{#toc-inverse-limits-profinite-groups-absolute-galois-groups}
- Energy Minimization, Moduli Spaces, and Flat Connections{#toc-energy-minimization-moduli-spaces-and-flat-connections}
- Instantons and Poles in Extended Supersymmetry{#toc-instantons-and-poles-in-extended-supersymmetry}
- Complexification, Embeddings, and Motivic Stabilizations{#toc-complexification-embeddings-and-motivic-stabilizations}
- Covariant, Geometric, Deformation Quantization (Gluing and Intersections){#toc-covariant-geometric-deformation-quantization-gluing-and-intersections}
- Linearization of Abelian Categories and Commutative
Geometry{#toc-linearization-of-abelian-categories-and-commutative-geometry}
- Zariski Topology, Borel subgroups{#toc-zariski-topology-borel-subgroups}
- Fields, Rings, Spectrum of Prime Ideals{#toc-fields-rings-spectrum-of-prime-ideals}
- Adeles and Ideles{#toc-adeles-and-ideles}
- Abelian Categories, Schemes{#toc-abelian-categories-schemes}
- Homotopy Abelianization of Homology{#toc-homotopy-abelianization-of-homology}
- Grothendieck Completion and K-Theory{#toc-grothendieck-completion-and-k-theory}
- Linearization of Automorphisms Under
Complexification{#toc-linearization-of-automorphisms-under-complexification}
- Connections as automorphisms{#toc-connections-as-automorphisms}
- Galois Group, Galois Representations{#toc-galois-group-galois-representations}
- Absolute Galois Group{#toc-absolute-galois-group}
- Moduli stack of elliptic curves and modular forms{#toc-moduli-stack-of-elliptic-curves-and-modular-forms}
- Automorphic forms{#toc-automorphic-forms}
- Moduli spaces, Sheaves, Stacks, Cohomology of Shtukas{#toc-moduli-spaces-sheaves-stacks-cohomology-of-shtukas}
- Linearization of Non-Abelian Manifolds Under Extended
Supersymmetry{#toc-linearization-of-non-abelian-manifolds-under-extended-supersymmetry}
- Differential Algebras, Lie gauges, Differential Galois Theory{#toc-differential-algebras-lie-gauges-differential-galois-theory}
- Connections as differential forms on tangent bundles{#toc-connections-as-differential-forms-on-tangent-bundles}
- Quotient spaces and Moduli Spaces{#toc-quotient-spaces-and-moduli-spaces}
- Non-Abelian Yang-Mills theory and Lagrangian Mechanics{#toc-non-abelian-yang-mills-theory-and-lagrangian-mechanics}
- Irreducible connections, Instantons and Monopoles{#toc-irreducible-connections-instantons-and-monopoles}
- Torsion, Holonomy, spectral and mass gaps{#toc-torsion-holonomy-spectral-and-mass-gaps}
- Donaldson Theory and Exotic R4{#toc-donaldson-theory-and-exotic-r4}
- Floer Homology{#toc-floer-homology}
- ADHM Monad Construction (Penrose twistor theory){#toc-adhm-monad-construction-penrose-twistor-theory}
- Seiberg-Witten Theory and Invariants{#toc-seiberg-witten-theory-and-invariants}
- Symplectic Geometry as weak
Abelianization{#toc-symplectic-geometry-as-weak-abelianization}
- Solder form, cotangent bundle{#toc-solder-form-cotangent-bundle}
- Hamiltonian Mechanics vs Lagrangian Mechanics{#toc-hamiltonian-mechanics-vs-lagrangian-mechanics}
- Symplectification, symplectic reduction{#toc-symplectification-symplectic-reduction}
- Interpreting symplectic reduction with Galois theory{#toc-interpreting-symplectic-reduction-with-galois-theory}
- Symplectic connection, deformation quantization{#toc-symplectic-connection-deformation-quantization}
- Covariant phase space{#toc-covariant-phase-space}
- Linearization with Graphs Under
Complexification{#toc-linearization-with-graphs-under-complexification}
- CW complex{#toc-cw-complex}
- Chains, Cochains, Cycles, Cocycles{#toc-chains-cochains-cycles-cocycles}
- Simplicial complex{#toc-simplicial-complex}
- Lefschetz fixed-point theorem{#toc-lefschetz-fixed-point-theorem}
- Cellular complex{#toc-cellular-complex}
- Laplacians and spectral theory{#toc-laplacians-and-spectral-theory}
- Triangulated categories{#toc-triangulated-categories}
- Quivers and Representations{#toc-quivers-and-representations}
- Dynkin Diagrams, Gabriel’s theorem, Root systems{#toc-dynkin-diagrams-gabriels-theorem-root-systems}
- Dessin d’enfant, Belyi’s theorem, moduli spaces{#toc-dessin-denfant-belyis-theorem-moduli-spaces}
- Linearization with Cohomology Derived
Invariants{#toc-linearization-with-cohomology-derived-invariants}
- de Rham Cohomology{#toc-de-rham-cohomology}
- Betti cohomology{#toc-betti-cohomology}
- Étale Cohomology{#toc-étale-cohomology}
- Weil cohomology{#toc-weil-cohomology}
- Crystalline cohomology{#toc-crystalline-cohomology}
- Hodge theory{#toc-hodge-theory}
- Chern–Weil theory{#toc-chernweil-theory}
- Grothendieck’s Dream - A Universal Cohomology and Derived
Invariant{#toc-grothendiecks-dream—a-universal-cohomology-and-derived-invariant}
- Chain-complex{#toc-chain-complex}
- Exact and Closed Sequences, Spectral Sequences, Filtrations{#toc-exact-and-closed-sequences-spectral-sequences-filtrations}
- Stable infinity-category{#toc-stable-infinity-category}
- Derived Categories, Coherent Sheaves{#toc-derived-categories-coherent-sheaves}
- Projective categories, Pure and Mixed Motives{#toc-projective-categories-pure-and-mixed-motives}
- Derived Category of Motives{#toc-derived-category-of-motives}
- Derived Invariants{#toc-derived-invariants}
- Furthest extent{#toc-furthest-extent}
- Grothendieck-Teichmüller space{#toc-grothendieck-teichmüller-space}
- Motivic Galois group, cosmic Galois group, renormalization{#toc-motivic-galois-group-cosmic-galois-group-renormalization}
- Motivic stablization of Symplectic manifolds{#toc-motivic-stablization-of-symplectic-manifolds}
- Shimura Variety, L-functions, and Zariski closure{#toc-shimura-variety-l-functions-and-zariski-closure}
- Nekrasov Instanton Partition Function, Young Diagrams{#toc-nekrasov-instanton-partition-function-young-diagrams}
- Triangulated categories of mixed motives{#toc-triangulated-categories-of-mixed-motives}
- Motives over simplicial schemes{#toc-motives-over-simplicial-schemes}
- Probability by Homology, Gromov p-widths{#toc-probability-by-homology-gromov-p-widths}
- Weinstein symplectic category{#toc-weinstein-symplectic-category}
- Tannakian Formalism{#toc-tannakian-formalism}
- Kähler Manifolds, hyperkähler manifold, Calabi–Yau manifold{#toc-kähler-manifolds-hyperkähler-manifold-calabiyau-manifold}
- Amplituhedron, poles, factorization, gauge quivers{#toc-amplituhedron-poles-factorization-gauge-quivers}
- Homological mirror symmetry{#toc-homological-mirror-symmetry}
- Topological Recursion{#toc-topological-recursion}
Compactification and Derived Representations
Fixed Points and Invariants
Linearization and Matrix Representations with Lie Groups
Abelianization and Completions
Sieves, Filtrations, Spectral Sequences
Projections, Ramifications, and Cohomology
Extensions, Closures, and Automorphisms
Quotients and Reductions
Diffusion, Gaussian Isotropy Group, Skeleton Category
Inverse Limits, Profinite Groups, Absolute Galois Groups
Energy Minimization, Moduli Spaces, and Flat Connections
Instantons and Poles in Extended Supersymmetry
Complexification, Embeddings, and Motivic Stabilizations
Covariant, Geometric, Deformation Quantization (Gluing and Intersections)
Linearization of Abelian Categories and Commutative Geometry
Zariski Topology, Borel subgroups
Fields, Rings, Spectrum of Prime Ideals
Adeles and Ideles
https://math.stackexchange.com/questions/25090/whats-the-significance-of-tates-thesis/25125#25125 https://math.stackexchange.com/questions/290847/what-do-ideles-and-adeles-look-like
Abelian Categories, Schemes
Homotopy Abelianization of Homology
Grothendieck Completion and K-Theory
Linearization of Automorphisms Under Complexification
Connections as automorphisms
Galois Group, Galois Representations
Absolute Galois Group
Moduli stack of elliptic curves and modular forms
Automorphic forms
Moduli spaces, Sheaves, Stacks, Cohomology of Shtukas
Linearization of Non-Abelian Manifolds Under Extended Supersymmetry
Differential Algebras, Lie gauges, Differential Galois Theory
Connections as differential forms on tangent bundles
Quotient spaces and Moduli Spaces
Non-Abelian Yang-Mills theory and Lagrangian Mechanics
Irreducible connections, Instantons and Monopoles
Torsion, Holonomy, spectral and mass gaps
Donaldson Theory and Exotic R4
Floer Homology
ADHM Monad Construction (Penrose twistor theory)
Seiberg-Witten Theory and Invariants
Symplectic Geometry as weak Abelianization
Solder form, cotangent bundle
Hamiltonian Mechanics vs Lagrangian Mechanics
Symplectification, symplectic reduction
Interpreting symplectic reduction with Galois theory
Symplectic connection, deformation quantization
Covariant phase space
Linearization with Graphs Under Complexification
permutation/symmetry group of roots