Related papers: Sheaves as oracle computations
The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for…
We define an equivalence relation among coherent sheaves on a projective variety called biliaison. We prove the existence of sheaves that are minimal in a biliaison class in a suitable sense, and show that all sheaves in the same class can…
We give a new geometric characterization of the motivic ramification filtration of reciprocity sheaves, by imitating a method used by Abbes and (Takeshi) Saito to study the ramification of torsors under finite \'etale groups. This new…
In classification and forecasting with tabular data, one often utilizes tree-based models. Those can be competitive with deep neural networks on tabular data and, under some conditions, explainable. The explainability depends on the depth…
We define the notion of a sheaf over a complex of groups. As an application, we give a criterion for the developability of a complex of groups. When the developability is witnessed by a morphism to $\mathrm{GL}(V)$ for some $V$, our…
Several notions of sheaf on various types of quantale have been proposed and studied in the last twenty five years. It is fairly standard that for an involutive quantale Q satisfying mild algebraic properties the sheaves on Q can be defined…
We give classifications of linear orbits of pairs of square matrices with non-vanishing discriminant polynomials over a field in terms of certain coherent sheaves with additional data on closed subschemes of the projective line. Our results…
Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…
It is usually not straightforward to work with the category of perverse sheaves on a variety using only its definition as a heart of a $t$-structure. In this paper, the category of perverse sheaves on a smooth toric variety with its orbit…
Many important theorems in differential topology relate properties of manifolds to properties of their underlying homotopy types -- defined e.g. using the total singular complex or the \v{C}ech nerve of a good open cover. Upon embedding the…
Given a field with a set of discrete valuations $V$, we show how the genus of a division algebra over the field is related to the genus of the residue algebras at various valuations in $V$ and the ramification data. When the division…
Nakano's "later" modality, inspired by G\"{o}del-L\"{o}b provability logic, has been applied in type systems and program logics to capture guarded recursion. Birkedal et al modelled this modality via the internal logic of the topos of…
Understanding predictions made by Machine Learning models is critical in many applications. In this work, we investigate the performance of two methods for explaining tree-based models- Tree Interpreter (TI) and SHapley Additive…
We present a functorial computation of the equivariant intersection cohomology of a hypertoric variety, and endow it with a natural ring structure. When the hyperplane arrangement associated with the hypertoric variety is unimodular, we…
In this article, we develop an explicit categorical realization of sheafification based on colimits, products, and subobjects, emphasizing its behavior in algebraic and topological-algebraic settings. We prove that if $\mathcal{C}$ is a…
We explore from an algebraic viewpoint the properties of the tree languages definable with a first-order formula involving the ancestor predicate, using the description of these languages as those recognized by iterated block products of…
Sampling theory has traditionally drawn tools from functional and complex analysis. Past successes, such as the Shannon-Nyquist theorem and recent advances in frame theory, have relied heavily on the application of geometry and analysis.…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
As data grows in size and complexity, finding frameworks which aid in interpretation and analysis has become critical. This is particularly true when data comes from complex systems where extensive structure is available, but must be drawn…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…