Related papers: Axiomatic Closure Operations, Phantom Extensions, …
Motivated by the Bass conjecture, we study finitely generated modules of finite injective dimension and the additional constraints they impose on the ambient ring. Beyond the Cohen--Macaulay property, the existence of such modules forces…
We prove a finiteness theorem and a comparison theorem in the theory of \'etale cohomology of rigid analytic varieties. By a result of Huber, for a quasi-compact separated morphism of rigid analytic varieties with target being of dimension…
This paper establishes the fundamental properties of the $s$-closures, a recently introduced family of closure operations on ideals of rings of positive characteristic. The behavior of the $s$-closure of homogeneous ideals in graded rings…
Consider a diagram of quasi-categories that admit and functors that preserve limits or colimits of a fixed shape. We show that any weighted limit whose weight is a projective cofibrant simplicial functor is again a quasi-category admitting…
This paper is a continuation of our work on the functional-analytic core of the classical Furstenberg-Zimmer theory. We introduce and study (in the framework of lattice-ordered spaces) the notions of total order-boundedness and uniform…
The large-order behaviour of QCD is dominated by renormalons. On the other hand renormalons do not occur in conformal theories, such as the one describing the infrared fixed-point of QCD at small beta_0 (the Banks--Zaks limit). Since the…
This article is concerned with nonzero modules of finite length and finite projective dimension over a local ring. We show the Loewy length of such a module is larger than the regularity of the ring whenever the ring is strict…
In this paper we give a new foundational, categorical formulation for operations and relations and objects parameterizing them. This generalizes and unifies the theory of operads and all their cousins including but not limited to PROPs,…
The purpose of this paper is to make a comprehensive connection between the basic results and properties derived from the two kinds of topologies (namely the $(\epsilon,\lambda)-$topology introduced by the author and the stronger locally…
We show that modularity and the gap condition make the holomorphic anomaly equation completely integrable for non-compact Calabi-Yau manifolds. This leads to a very efficient formalism to solve the topological string on these geometries in…
For a Cohen-Macaulay ring $R$, we exhibit the equivalence of the bounded derived categories of certain resolving subcategories, which, amongst other results, yields an equivalence of the bounded derived category of finite length and finite…
We derive new bounds on higher-dimension operator coefficients in four-dimensional Einstein-Maxwell theory. Positivity of classically-generated corrections to the Wald entropy of thermodynamically stable, rotating dyonic black holes implies…
Over $d$-dimensional Cohen-Macaulay rings with a canonical module, $d$-cotilting classes containing the maximal and balanced big Cohen-Macaulay modules are classified. Particular emphasis is paid to the direct limit closure of the balanced…
Under a suitable notion of equivalence of integral densities we prove a $\Gamma$-closure theorem for integral functionals: The limit of a sequence of $\Gamma$-convergent families of such functionals is again a $\Gamma$-convergent family.…
A resolution of the identity due to canonical coherent states is often proven in the weak operator topology. However, such a resolution with an integral symbol is typically supposed to hold in the strong operator topology associated with…
By finding a p-adic obstruction, we construct many examples of positive characteristic complete noetherian local rings which do not admit any module-finite Cohen-Macaulay extension. These examples should be contrasted with a result of…
Every CSP(B) for a finite structure B is either in P or it is NP-complete but the proofs of the finite-domain CSP dichotomy by Andrei Bulatov and Dimitryi Zhuk not only show the computational complexity separation but also confirm the…
We prove two theorems about Goodwillie calculus and use those theorems to describe new models for Goodwillie derivatives of functors between pointed compactly-generated infinity-categories. The first theorem say that the construction of…
We present a simple resolution proof system for higher-order constrained Horn clauses (HoCHC) - a system of higher-order logic modulo theories - and prove its soundness and refutational completeness w.r.t. the standard semantics. As…
The landmark Levy-Solovay Theorem limits the kind of large cardinal embeddings that can exist in a small forcing extension. Here I announce a generalization of this theorem to a broad new class of forcing notions. One consequence is that…