G. Vooys

activity

20192026

collaborators

9 papers

math.AG2026

A Deep Dive Into the Tangent Category of Schemes

Geoff Vooys

In this largely expository paper we provide a deep and explicit exploration and exposition of the tangent structure on the category of schemes $Sch_{/ S}$ whose tangent fun…

math.CT2025

Important Classes of Morphisms and the Relative Cotangent Sequence in Tangent Categories

Jean-Simon Pacaud Lemay, Geoff Vooys

In this paper we provide a deep and systematic study of what it means to be an immersion, a submersion, a local diffeomorphism, and unramified in a tangent category. We also give a…

math.AG2024

On the Equivariant Derived Category of Perverse Sheaves

Geoff Vooys

In this paper we extend Beilinson's realization formalism for triangulated categories and filtered triangulated categories to a pseudofunctorial and pseudonatural setting. As a con…

math.AG2024

Categories of Pseudocones and Equivariant Descent

Geoff Vooys

In this monograph we provide an in-depth and systematic study of pseudolimits of pseudofunctors $F : C^{o p} \to Cat$ in the $2$ -category of categories where $\ma…

math.CT2023

Pseudolimits for Tangent Categories with Applications to Equivariant Algebraic and Differential Geometry

Dorette Pronk, Geoff Vooys

In this paper we show that if $C$ is a category and if $F : C^{op} \to Cat$ is a pseudofunctor such that for each object $X$ of $\m…

math.CT2023

Tangent Ind-Categories

Geoff Vooys

In this paper we show that if $C$ is a tangent category then the Ind-category $Ind (C)$ is a tangent category as well with a tangent structure whi…

math.AG2021

Equivariant Functors and Sheaves

Geoff Vooys

In this thesis we study two main topics which culminate in a proof that four distinct definitions of the equivariant derived category of a smooth algebraic group $G$ acting on a va…

math.NT2020

Serre-Hazewinkel Local Class Field Theory and a Geometric Proof of the Local Langlands Correspondence for $GL (1)$

Geoff Vooys

In this expository paper we provide a geometric proof of the local Langlands Correspondence for the groups $GL_{1}$ defined over $p$ -adic fields $K$ . We do this by r…

math.AG2019

The Greenberg Functor is Site Cocontinuous

Geoff Vooys

In this paper we show that it is possible to define a topology on the category of formal schemes over a ring of $p$ -adic integers such that the left adjoint of the Greenberg Transf…

A Deep Dive Into the Tangent Category of Schemes

Important Classes of Morphisms and the Relative Cotangent Sequence in Tangent Categories

On the Equivariant Derived Category of Perverse Sheaves

Categories of Pseudocones and Equivariant Descent

Pseudolimits for Tangent Categories with Applications to Equivariant Algebraic and Differential Geometry

Tangent Ind-Categories

Equivariant Functors and Sheaves

Serre-Hazewinkel Local Class Field Theory and a Geometric Proof of the Local Langlands Correspondence for GL(1)

The Greenberg Functor is Site Cocontinuous

Serre-Hazewinkel Local Class Field Theory and a Geometric Proof of the Local Langlands Correspondence for $GL (1)$