In type III1 factors the ultrapower of the spectral subspace M(σ^φ, F) is a proper subset of the spectral subspace of the ultrapowered algebra.
Some theorems on locally product Riemann - ian spaces
9 Pith papers cite this work. Polarity classification is still indexing.
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The bicentralizer problem for III1 factors has a positive solution if and only if the bicentralizer functor is a zeroset in the theory of III1 factors, and the class of such factors with trivial bicentralizer is ∀∃-axiomatizable.
New LTO axioms ensure Haag duality for cones and reflection positivity, verified for all known topologically ordered commuting projector models.
Orbital integrals on unitary groups over local fields in positive characteristic converge absolutely.
For smooth projective X of dim d≥5, D^b(X^[3]) admits a semi-orthogonal sequence of length binom(d-3,2) with each term equivalent to D(X) via FM transform from a Grassmannian bundle G over X.
The condensed fundamental group of Spec(Z) is non-trivial, hence Spec(Z) is not condensed contractible.
A new fibration theorem implies solvable descent, solving the Grunwald problem for solvable groups up to the Brauer-Manin obstruction.
Killing tensors on products of Riemannian manifolds with one compact factor are reducible sums of factor tensors.
Shape theory for condensed anima recovers classical shape for paracompact compactly generated and locally contractible spaces while extending sheaf-condensed cohomology comparisons.
citing papers explorer
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Ultrapowers of spectral subspaces
In type III1 factors the ultrapower of the spectral subspace M(σ^φ, F) is a proper subset of the spectral subspace of the ultrapowered algebra.
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Model theory and Connes' bicentralizer problem
The bicentralizer problem for III1 factors has a positive solution if and only if the bicentralizer functor is a zeroset in the theory of III1 factors, and the class of such factors with trivial bicentralizer is ∀∃-axiomatizable.
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Local topological order, Haag duality, and reflection positivity
New LTO axioms ensure Haag duality for cones and reflection positivity, verified for all known topologically ordered commuting projector models.
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Convergence of orbital integrals on unitary groups in positive characteristic
Orbital integrals on unitary groups over local fields in positive characteristic converge absolutely.
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A Semi-orthogonal Sequence in the Derived Category of the Hilbert Scheme of Three Points
For smooth projective X of dim d≥5, D^b(X^[3]) admits a semi-orthogonal sequence of length binom(d-3,2) with each term equivalent to D(X) via FM transform from a Grassmannian bundle G over X.
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On Galois categories and condensed contractible schemes
The condensed fundamental group of Spec(Z) is non-trivial, hence Spec(Z) is not condensed contractible.
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Solvable Descent and the Grunwald Problem for Solvable Groups
A new fibration theorem implies solvable descent, solving the Grunwald problem for solvable groups up to the Brauer-Manin obstruction.
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Killing tensors on reducible spaces
Killing tensors on products of Riemannian manifolds with one compact factor are reducible sums of factor tensors.
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Shape theory for condensed anima
Shape theory for condensed anima recovers classical shape for paracompact compactly generated and locally contractible spaces while extending sheaf-condensed cohomology comparisons.