My 23 main mathematical theorems

As a mathematical and theoretical physicist, I have proved a lot of theorems and assertions. This is a LIST of my 23 most relevant original theorems:

• Modification of the abstract De Rham theorem
• Generalization of the Serra – Swan theorem for non-compact manifolds
• Serra – Swan-like theorem for graded manifolds
• Theorem on the cohomology of differential forms on an infinite order jet manifold
• Theorem on the cohomology of the variational bicomplex on fibre bundles
• Theorem on the cohomology of the Grassmann-graded variational bicomplex on graded bundles
• Solution of the global inverse problem of the calculus of variations in a very general setting
• Global variational formula
• First Noether theorem in a general setting of Grassmann-graded Lagrangians and their generalized  supersymmetries
• Theorem on the superpotential form of a gauge symmetry current in a general setting
• Theorem on the Koszul – Tate chain complex of higher-stage Noether identities of a generic differential operator on a fibre bundle
• Theorem on the Koszul – Tate chain complex of Noether identities of a generic reducible degenerate Grassmann-graded Lagrangian
• The inverse and direct second Noether theorems in a very general setting
• Theorem on the iterated BRST cohomology
• Theorem on the canonical decomposition of the jet bundle J^1C -> C of a bundle C of principal connections
• Comprehensive relations between Lagrangian and covariant (polysymplectic) Hamiltonian formalisms in a case of semiregular Lagrangians
• Conditions of a dynamic algebra to be a partially integrable system on a Poisson manifold
• Generalization of the Liouville – Arnold theorem on completely integrable systems to a case of partically integrable systems on a Poisson manifold and its non-compact invariant submanifolds
• Generalization of the Poincare – Lyapounov – Nekhoroshev theorem on partially integrable systems to a case of non-compact invariant submanifolds
• Theorem on global action-angle coordinates of partially integrable systems in a general case of invariant submanifolds which need not be compact
• Generalization of the Mishchenko – Fomenko theorem on superintegrable systems to a case of non-compact invariant submanifolds
• Theorem on global generalized action-angle coordinates of superintegrable systems in a case of possibly non-compact invariant submanifolds
• Theorem on reduction of a principal superbundle in the category of G-supermanifolds

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