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Automorphisms, Connections, and Motivic Cohomology |
- 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}
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
permutation/symmetry group of roots