Related papers: What makes a multi-complex exact?
We prove completeness results for a wide variety of intuitionistic conditional logics. We do so by first using a canonical model construction obtain completeness with respect to descriptive conditional frames, and then introducing the…
Perfect quadratic forms give a toroidal compactification of the moduli space of principally polarized abelian g-folds that is Q-factorial and whose ample classes are characterized, over any base. In characteristic zero it has canonical…
In this paper, we generalize the notions of perfect matchings, perfect 2-matchings to perfect k-matchings and give a necessary and sufficient condition for existence of perfect k-matchings. For bipartite graphs, we show that this k-matching…
We describe a rigorous computer algorithm for attempting to construct an explicit, discretized metric for which a complex polynomial map is expansive on a given neighborhood of its Julia set. We show construction of such a metric proves the…
We give an elementary construction of the exact completion of a weakly lex category for categories enriched in the cartesian closed category $\mathsf{Pos}$ of partially ordered sets. Paralleling the ordinary case, we characterize categories…
We give a criterion for a collection of polynomials to be a universal Gr\"{o}bner basis for an ideal in terms of the multidegree of the closure of the corresponding affine variety in $(\mathbb{P}^1)^N$. This criterion can be used to give…
Necessary and sufficient conditions are presented for the (first-order) theory of a universal class of algebraic structures (algebras) to admit a model completion, extending a characterization provided by Wheeler. For varieties of algebras…
This paper calculates the number of full exceptional collections modulo an action of a group as the set generated by spherical twists for an abelian category of coherent sheaves on an orbifold projective line with a zero orbifold Euler…
We give necessary conditions for perfection of some families of odd numbers with special multiplicative forms. Extending earlier work of Steuerwald, Kanold, McDaniel et al.
We introduce a very natural topology on the set of total orderings of monomials of any algebra having a countable basis over a field. This topological space and some notable subspaces are compact. This topological framework allows us to…
A structure theorem is proved for strongly holonomic modules over a quantum torus (a crossed product of a field with a free abelian group in which the field is central). This can be applied to give a structure theorem for finitely presented…
We generalize the notion of semi-universality in the classical deformation problems to the context of derived deformation theories. A criterion for a formal moduli problem to be semi-prorepresentable is produced. This can be seen as an…
We prove exactly that the squared entanglement of formation, which quantifies the bipartite entanglement, obeys a general monogamy inequality in an arbitrary multiqubit mixed state. Based on this kind of exotic monogamy relation, we are…
We show that every additive category with kernels and cokernels admits a maximal exact structure. Moreover, we discuss two examples of categories of the latter type arising from functional analysis.
Let $X$ be a finite-dimensional, noetherian scheme. Antieau, Gepner and Heller conjectured that its derived category of perfect complexes has a bounded t-structure if and only if $X$ is regular. We prove a generalization, and to do so we…
We consider Cayley sum graphs over the cyclic group $\mathbb{Z}_n$ and aim to explore several necessary and sufficient conditions for the existence of total perfect codes in these graphs. Specifically, we examine various cases for the…
Improved local and global versions of the effective Nullstellensatz for ideal sheaves on non-singular complex varieties are obtained, based on a new invariant motivated by the notion of finite type from the theory of several complex…
We investigate various homotopy invariant formulations of commutative algebra in the context of rational homotopy theory. The main subject is the complete intersection condition, where we show that a growth condition implies a structure…
We formalise, in Coq, the opening sections of Parity Complexes [Street1991] up to and including the all important excision of extremals algorithm. Parity complexes describe the essential combinatorial structure exhibited by simplexes, cubes…
We derive a family of correctness conditions for complex Langevin simulations. In particular, we show that if in a given theory the expectation values of all observables within a particular space satisfy the theory's Schwinger-Dyson…