40 citations · 84 across the 18 of their papers we have counts for
18 papers
Categorification of the localized intersection product and Bloch conductor formula
Dario Beraldo, Massimo Pippi
We categorify the localized intersection product on arithmetic schemes defined by Kato--Saito in \cite{katosaito04}. As an application, we prove a generalization of Bloch conductor…
Coherent sheaves, sheared D-modules, and Hochschild cochains
Dario Beraldo, Kevin Lin, Wyatt Reeves
We show that the category of ind-coherent sheaves on a quasi-smooth scheme is naturally tensored over the category of sheared D-modules on its shifted cotangent bundle, commuting w…
Proof of the Deligne-Milnor conjecture
Dario Beraldo, Massimo Pippi
We apply methods of derived and non-commutative algebraic geometry to understand ramification phenomena on arithmetic schemes. As an application, we prove the Deligne-Milnor conjec…
Proof of the geometric Langlands conjecture IV: ambidexterity
D. Arinkin, D. Beraldo, L. Chen +5
This paper performs the following steps toward the proof of GLC in the de Rham setting: (i) We deduce GLC for G=GL_n; (ii) We prove that the Langlands functor L_G constructed in [G…
Proof of the geometric Langlands conjecture II: Kac-Moody localization and the FLE
D. Arinkin, D. Beraldo, J. Campbell +6
This paper is the second in a series of five that together prove the geometric Langlands conjecture. Our goals are two-fold: (1) Formulate and prove the Fundamental Local Equivalen…
Non-commutative nature of -adic vanishing cycles
Dario Beraldo, Massimo Pippi
Let be a flat, proper and regular scheme over a strictly henselian discrete valuation ring. We prove that the singularity category of the special fiber with its…
Non-commutative intersection theory and unipotent Deligne-Milnor formula
Dario Beraldo, Massimo Pippi
We apply methods of derived and non-commutative algebraic geometry to understand intersection theoretic phenomena on arithmetic schemes. Specifically, we categorify Bloch's interse…
Automorphic Gluing
Dario Beraldo, Lin Chen
We prove a gluing theorem on the automorphic side of the geometric Langlands correspondence: roughly speaking, we show that the difference between a…
On the geometric Ramanujan conjecture
Dario Beraldo
In this paper we prove two results pertaining to the (unramified and global) geometric Langlands program. The first result is an analogue of the Ramanujan conjecture: any cuspidal…
Deligne-Lusztig duality on the stack of local systems
Dario Beraldo
In the setting of the geometric Langlands conjecture, we argue that the phenomenon of divergence at infinity on Bun_G (that is, the difference between -extensions and -extens…
Tempered D-modules and Borel-Moore homology vanishing
Dario Beraldo
We characterize the tempered part of the automorphic Langlands category D-mod(Bun_G) using the geometry of the big cell in the affine Grassmannian. We deduce that, for non-abel…
The spectral gluing theorem revisited
Dario Beraldo
We strengthen the gluing theorem occurring on the spectral side of the geometric Langlands conjecture. While the latter embeds into a category glued out of 'Fourie…
The topological chiral homology of the spherical category
Dario Beraldo
We consider the spherical DG category attached to an affine algebraic group . By definition, consists of ind-coherent sheaves of the stack o…
Sheaves of categories with local actions of Hochschild cochains
Dario Beraldo
The notion of Hochschild cochains induces an assignment from , affine DG schemes, to monoidal DG categories. We show that this assignment extends, under some appropriate finit…
Contractibility of the space of generic opers for classical groups
Dario Beraldo, David Kazhdan, Tomer M. Schlank
Let be a reductive group and a smooth projective curve. We prove that, for classical and an arbitrary -local system on , the space $\overline{\operatorname{Op…
The center of the categorified ring of differential operators
Dario Beraldo
Let \Y be a derived algebraic stack satisfying some mild conditions. The purpose of this paper is three-fold. First, we introduce and study H(\Y), a monoidal DG category that might…
On the extended Whittaker category
Dario Beraldo
Let be a connected reductive group, with connected center, and a smooth complete curve, both defined over an algebraically closed field of characteristic zero. Let $\operat…
Loop group actions on categories and Whittaker invariants
Dario Beraldo
We develop some aspects of the theory of -modules on ind-schemes of pro-finite type. These notions are used to define -modules on (algebraic) loop groups and, consequently, a…