104 citations · 460 across the 24 of their papers we have counts for
27 papers
Sharp global stability for the hard-sphere Boltzmann equation near equilibrium
Xuwen Chen, Shunlin Shen, Zhifei Zhang
We study the hard-sphere Boltzmann equation near a global Maxwellian and have found the bifurcation between the stability and instability in Sobolev space. We prove a s…
Harmonic Norms on Quiver Representations over Non-Archimedean Fields
Oren Ben-Bassat
Let be any complete non-Archimedean field, not necessarily spherically complete. We prove that every polystable representation of a finite quiver over admits a split harmon…
Arithmetic field theory via pro-p duality groups
Nadav Gropper, Oren Ben-Bassat
Using the theory of pro-p groups and relative Poincaré duality, we define a type of cobordism category well suited to arithmetic topology. We completely classify topological quantu…
A Perspective on the Foundations of Derived Analytic Geometry
Oren Ben-Bassat, Jack Kelly, Kobi Kremnizer
We show how one can do algebraic geometry with respect to the category of simplicial objects in an exact category. As a biproduct, we get a theory of derived analytic geometry.
Moduli stacks of Higgs bundles on stable curves
Oren Ben-Bassat, Sourav Das, Tony Pantev
In this article, we construct a flat degeneration of the derived moduli stack of Higgs bundles on smooth curves using the stack of expanded degenerations of Jun Li. We show that th…
Blow-ups and normal bundles in connective and nonconnective derived geometries
Oren Ben-Bassat, Jeroen Hekking
This work presents a generalization of derived blow-ups and of the derived deformation to the normal bundle from derived algebraic geometry to any geometric context. The latter is…
Analytification, localization and homotopy epimorphisms
Oren Ben-Bassat, Devarshi Mukherjee
We study the interaction between various analytification functors, and a class of morphisms of rings, called homotopy epimorphisms. An analytification functor assigns to a simplici…
Fréchet Modules and Descent
Oren Ben-Bassat, Kobi Kremnizer
We study several aspects of the study of Ind-Banach modules over Banach rings thereby synthesizing some aspects of homological algebra and functional analysis. This includes a stud…
Analytic geometry over F_1 and the Fargues-Fontaine curve
Federico Bambozzi, Oren Ben-Bassat, Kobi Kremnizer
This paper develops a theory of analytic geometry over the field with one element. The approach used is the analytic counter-part of the Toen-Vaquie theory of schemes over F_1, i.e…
Bounded linear endomorphisms of rigid analytic functions
Konstantin Ardakov, Oren Ben-Bassat
Let be a field of characteristic zero complete with respect to a non-trivial, non-Archimedean valuation. We relate the sheaf of infinite order different…
Perversely categorified Lagrangian correspondences
Lino Amorim, Oren Ben-Bassat
In this article, we construct a -category of Lagrangians in a fixed shifted symplectic derived stack S. The objects and morphisms are all given by Lagrangians living on various…
Stein Domains in Banach Algebraic Geometry
Federico Bambozzi, Oren Ben-Bassat, Kobi Kremnizer
In this article we give a homological characterization of the topology of Stein spaces over any valued base field. In particular, when working over the field of complex numbers, we…
Dagger Geometry As Banach Algebraic Geometry
Federico Bambozzi, Oren Ben-Bassat
In this article, we apply the approach of relative algebraic geometry towards analytic geometry to the category of bornological and Ind-Banach spaces (non-Archimedean or not). We a…
Non-Archimedean analytic geometry as relative algebraic geometry
Oren Ben-Bassat, Kobi Kremnizer
We show that Berkovich analytic geometry can be viewed as relative algebraic geometry in the sense of Toën--Vaquié--Vezzosi over the category of non-Archimedean Banach spaces. For…
A 'Darboux Theorem' for shifted symplectic structures on derived Artin stacks, with applications
Oren Ben-Bassat, Christopher Brav, Vittoria Bussi +1
This is the fifth in a series arXiv:1304.4508, arXiv:1305,6302, arXiv:1211.3259, arXiv:1305.6428 on the '-shifted symplectic derived algebraic geometry' of Pantev, Toen, Vaquie…
Multiple Derived Lagrangian Intersections
Oren Ben-Bassat
We give a new way to produce examples of Lagrangians in shifted symplectic derived stacks, based on multiple intersections. Specifically, we show that an m-fold fiber product of La…
Milnor descent for cohesive dg-categories
Oren Ben-Bassat, Jonathan Block
We show that the functor from curved differential graded algebras to differential graded categories, defined by the second author in [B], sends Cartesian diagrams to homotopy Carte…
Berkovich Spaces and Tubular Descent
O. Ben-Bassat, M. Temkin
We consider an algebraic variety X together with the choice of a subvariety Z. We show that any coherent sheaf on X can be constructed out of a coherent sheaf on the formal neighbo…
Moduli Stacks of Bundles on Local Surfaces
Oren Ben-Bassat, Elizabeth Gasparim
We give an explicit groupoid presentation of certain stacks of vector bundles on formal neighborhoods of rational curves inside algebraic surfaces. The presentation involves a Möbi…
Equivariant Gerbes on Complex Tori
Oren Ben-Bassat
We explore a new direction in representation theory which comes from holomorphic gerbes on complex tori. The analogue of the theta group of a holomorphic line bundle on a (compact)…
Meromorphic Line Bundles and Holomorphic Gerbes
Edoardo Ballico, Oren Ben-Bassat
We show that any complex manifold that has a divisor whose normalization has non-zero first Betti number either has a non-trivial holomorphic gerbe which does not trivialize meromo…
Cohomology Groups of Deformations of Line Bundles on Complex Tori
O. Ben-Bassat, N. Solomon
The cohomology groups of line bundles over complex tori (or abelian varieties) are classically studied invariants of these spaces. In this article, we compute the cohomology groups…
Gerbes and the Holomorphic Brauer Group of Complex Tori
Oren Ben-Bassat
The purpose of this paper is to develop the theory of holomorphic gerbes on complex tori in a manner analogous to the classical theory for line bundles. In contrast to past studies…
Twisting Derived Equivalences
Oren Ben-Bassat
We introduce a new method for ``twisting'' relative equivalences of derived categories of sheaves on two spaces over the same base. The first aspect of this is that the derived cat…