Related papers: Produit tensoriel compl\'et\'e et platitude

We prove the equivalence of two tensor products over a category of W*-algebras with normal (not necessarily unital) *-homomorphisms, defined by Guichardet and Dauns, respectively. This structure differs from the standard tensor product…

Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…

Let $R$ be a complete discrete valuation ring with fraction field $K$ and with algebraically closed residue field. Let $X$ be a faithfully flat $R$-scheme of finite type of relative dimension 1 and $G$ be any affine $K$-group scheme of…

We prove a $p$-adic analog of Kunz's theorem: a $p$-adically complete noetherian ring is regular exactly when it admits a faithfully flat map to a perfectoid ring. This result is deduced from a more precise statement on detecting finiteness…

We prove explicit formulas for Chern classes of tensor products of vector bundles, with coefficients given by certain universal polynomials in the ranks of the two bundles.

We introduce and extend the outer product and contractive product of tensors and matrices, and present some identities in terms of these products. We offer tensor expressions of derivatives of tensors, focus on the tensor forms of…

An example is given of a compact absolute retract that is not a Hilbert cube manifold but whose second symmetric porduct is the Hilbert cube. A factor theorem is given for nth symmetric product of the cartesian product of any absolute…

We provide necessary and/or sufficient conditions for the stable Hom functors to be finitely presented. When the covariant Hom functor modulo projectives is finitely presented, its defect is isomorphic to the Bass torsion of the fixed…

We formalize in Lean the following foundational result in commutative algebra: Let $R \to S$ be a faithfully flat map of (not necessarily noetherian) commutative rings, and let $P$ be an arbitrary $R$-module. Then $P$ is projective over $R$…

We investigate cases where the finite dual coalgebra of a twisted tensor product of two algebras is a cotwisted tensor product of their respective finite dual coalgebras. This is achieved by interpreting the finite dual as a topological…

C.Swartz' result on tensor product measures is reviewed with proofs from the scratch.

We obtain a family of explicit "polyhedral" combinatorial expressions for multiplicities in the tensor product of two simple finite-dimensional modules over a complex semisimple Lie algebra. Here "polyhedral" means that the multiplicity in…

We show that any homomorphism between Noetherian $F$-finite rings can be factored into a regular morphism between Noetherian $F$-finite rings followed by a surjection. This result establishes an analog of the 'smooth-by-surjective'…

We solve the classifying problem raised by Fischer and Marsden for Bach flat static spaces. We also prove the conjecture about critical point equations proposed by Besse for Bach flat manifolds. Particularly in dimension 3, we derive an…

We address the problem of when the tensor product of two finitely generated modules over a Cohen-Macaulay local ring is Ulrich in the generalized sense of Goto et al., and in particular in the original sense from the 80's. As applications,…

Over a right-noetherian algebra admitting a dualizing complex, any left-module with finite flat dimension also has finite projective dimension.

We show that some more results from the literature are particular cases of the so-called "invariance under twisting" for twisted tensor products of algebras, for instance a result of Beattie-Chen-Zhang that implies the Blattner-Montgomery…

We introduce vector-valued Eidelheit sequences and obtain a characterization that generalizes Eidelheit's classical theorem (Studia Math. 6 (1936), 139-148). As an application, we discuss criteria for non $B$-completeness of completed…

A new connection between two different necessary conditions for a polymatroid to be linearly representable is presented. Specifically, we prove that the existence of a tensor product with the uniform matroid of rank two on three elements…

In this article we reduce the geometric stability conjecture for the scalar torus rigidity theorem to the conformal case via the Yamabe problem. Then we are able to prove the case where a sequence of Riemannian manifolds is conformal to a…