41 citations · 127 across the 18 of their papers we have counts for
21 papers
Flops and Hilbert schemes of space curve singularities
Duiliu-Emanuel Diaconescu, Mauro Porta, Francesco Sala +1
Using pagoda flop transitions between smooth projective threefolds, a relation is derived between the Euler numbers of moduli spaces of stable pairs which are scheme-theoretically…
Topological exodromy with coefficients
Mauro Porta, Jean-Baptiste Teyssier
The exodromy equivalence relates the derived -category of constructible sheaves on a stratified space (X,P) with the -category of representations of the exit-paths…
Non-archimedean Gromov-Witten invariants
Mauro Porta, Tony Yue YU
Motivated by mirror symmetry and the enumeration of holomorphic disks, we construct the theory of Gromov-Witten invariants in the setting of non-archimedean analytic geometry. We b…
Cohomological Hall algebras, their categorification, and their representations via torsion pairs
Duiliu-Emanuel Diaconescu, Mauro Porta, Francesco Sala
In this paper we provide a systematic way of producing representations of cohomological, K-theoretical and categorified Hall algebras, and study the output of our construction in s…
GAGA problems for the Brauer group via derived geometry
Federico Binda, Mauro Porta
This paper is dedicated to a further study of derived Azumaya algebras. The first result we obtain is a Beauville-Laszlo-style property for such objects (considered up to Morita eq…
The homotopy-invariance of constructible sheaves
Peter J. Haine, Mauro Porta, Jean-Baptiste Teyssier
The purpose of this paper is to explain why the functor that sends a stratified topological space to the -category of constructible (hyper)sheaves on with coefficie…
McKay correspondence, cohomological Hall algebras and categorification
Duiliu-Emanuel Diaconescu, Mauro Porta, Francesco Sala
Let denote the canonical resolution of the two dimensional Kleinian singularity of type ADE. In the present paper, we establish isomorphisms between the cohomo…
Non-archimedean quantum K-invariants
Mauro Porta, Tony Yue Yu
We construct quantum K-invariants in non-archimedean analytic geometry. Contrary to the classical approach in algebraic geometry via perfect obstruction theory, we build on our pre…
Derived Non-archimedean analytic Hilbert space
Jorge António, Mauro Porta
In this short paper we combine the representability theorem introduced in [17, 18] with the theory of derived formal models introduced in [2] to prove the existence representabilit…
Two-dimensional categorified Hall algebras
Mauro Porta, Francesco Sala
In the present paper, we introduce two-dimensional categorified Hall algebras of smooth curves and smooth surfaces. A categorified Hall algebra is an associative monoidal structure…
Analytification of mapping stacks
Julian Holstein, Mauro Porta
Derived mapping stacks are a fundamental source of examples of derived enhancements of classical moduli problems. For instance, they appear naturally in Gromov-Witten theory and in…
Derived Hom spaces in rigid analytic geometry
Mauro Porta, Tony Yue Yu
We construct a derived enhancement of Hom spaces between rigid analytic spaces. It encodes the hidden deformation-theoretic informations of the underlying classical moduli space. T…
Representability theorem in derived analytic geometry
Mauro Porta, Tony Yue Yu
We prove the representability theorem in derived analytic geometry. The theorem asserts that an analytic moduli functor is a derived analytic stack if and only if it is compatible…
The derived Riemann-Hilbert correspondence
Mauro Porta
In this short paper we prove a derived version of the Riemann-Hilbert correspondence of Deligne and Simpson. Our generalization is twofold: on one side we consider families of repr…
Formal gluing along non-linear flags
Benjamin Hennion, Mauro Porta, Gabriele Vezzosi
In this paper we prove formal glueing along an arbitrary closed substack of an arbitrary Artin stack (locally of finite type over a field ), for the stacks of (almost) p…
Derived non-archimedean analytic spaces
Mauro Porta, Tony Yue Yu
We propose a derived version of non-archimedean analytic geometry. Intuitively, a derived non-archimedean analytic space consists of an ordinary non-archimedean analytic space equi…
Derived complex analytic geometry II: square-zero extensions
Mauro Porta
We continue the explorations of derived \canal geometry started in [DAG-IX] and in http://arxiv.org/abs/1506.09042. We describe the category of -modules over a derive…
Comparison results for derived Deligne-Mumford stacks
Mauro Porta
In this short note we write down a comparison between the notion of derived Deligne-Mumford stack in the sense of B. Toën and G. Vezzosi [HAG-II] and the one introduced by J. Lurie…
Derived complex analytic geometry I: GAGA theorems
Mauro Porta
In this paper, we expand the foundations of derived complex analytic geometry introduced in [DAG-IX] by J. Lurie. We start by studying the analytification functor and its propertie…
Higher analytic stacks and GAGA theorems
Mauro Porta, Tony Yue Yu
We develop the foundations of higher geometric stacks in complex analytic geometry and in non-archimedean analytic geometry. We study coherent sheaves and prove the analog of Graue…
Infinitesimal and square-zero extensions of simplicial algebras
Mauro Porta, Gabriele Vezzosi
We introduce the notions of infinitesimal extension and square-zero extension in the context of simplicial commutatie algebras. We next investigate their mutual relationship and we…