Related papers: Derived analytic geometry: Derived K\"ahler space …

In this paper, we prove a general theorem concerning the analyticity of the closure of a subspace defined by a family of variations of mixed Hodge structures, which includes the analyticity of the zero loci of degenerating normal functions.…

The theory uses methods and language of linear algebra to study nonlinear spaces. These techniques can be used particularly to describe analytic geometry of non-linear elliptic, hyperbolic, De Sitter and Anti de Sitter spaces. The main…

We construct a new cohomology theory for proper smooth (formal) schemes over the ring of integers of C_p. It takes values in a mixed-characteristic analogue of Dieudonne modules, which was previously defined by Fargues as a version of…

In this paper, we study Frobenius structures in higher dimensional $p$-adic analytic geometry and the corresponding $p$-adic functional analysis. This will build up foundations for further study on some generalized cohomology of Frobenius…

In this PhD thesis, we give a new geometric approach to higher Teichm\"uller theory. In particular we construct a geometric structure on surfaces, generalizing the complex structure, and we explore its link to Hitchin components. The…

We construct two algebraic versions of homotopy theory of rational disconnected topological spaces, one based on differential graded commutative associative algebras and the other one on complete differential graded Lie algebras. As an…

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 on the stable $\infty$-category…

We develop a formulation for non-commutative derived analytic geometry built from differential graded (dg) algebras equipped with free entire functional calculus (FEFC), relating them to simplicial FEFC algebras and to locally…

This note is supposed to answer some questions on deformation theory in derived algebraic geometry. We show that derived algebraic geometry allows for a geometrical interpretation of the full cotangent complex and gives a natural setting…

Let $K$ be a finite extension of $\mathbb{Q}_p$. We prove that the arithmetic $p$-adic pro-\'etale cohomology of smooth partially proper spaces over $K$ satisfies a duality, as conjectured by Colmez, Gilles and Nizio{\l}. We derive it from…

We construct a generalization of the Dolbeault-Grothendieck resolution on a singular complex space. The same construction yields, for each morphism of analytic spaces, a pullback mapping between the respective Dolbeault-Grothendieck…

Hodge theory associates to a smooth projective variety over $\mathbb{C}$ a piece of linear algebra information, called a $\mathbb{Q}$-Hodge structure. Conversely, it is a natural question which abstract $\mathbb{Q}$-Hodge structures arise…

This is a book on derived foliations, that are a generalisation of classical foliations in the context of derived geometry. The text starts with the basic definitions and constructions, then explore foliated cohomology (with crystal…

After briefly reviewing the methods that allow us to derive consistently new Lie (super)algebras from given ones, we consider enlarged superspaces and superalgebras, their relevance and some possible applications.

Let $R$ be a Banach ring. We prove that the category of chain complexes of complete bornological $R$-modules (and several related categories) is a derived algebraic context in the sense of Raksit. We then use the framework of derived…

We use derived localization of the bar and nerve constructions to provide simple proofs of a number of results in algebraic topology. This includes a recent generalization of Adams' cobar-construction to the non-simply connected case, and a…

A framework to systematically decouple high order elliptic equations into combination of Poisson-type and Stokes-type equations is developed. The key is to systematically construct the underling commutative diagrams involving the complexes…

In this paper we first consider the Hamiltonian action of a compact connected Lie group on an $H$-twisted generalized complex manifold $M$. Given such an action, we define generalized equivariant cohomology and generalized equivariant…

We study jet schemes and arc spaces in the context of derived algebraic geometry. Explicitly, we consider the jet and arc functors in the category of schemes and study their animations to the category of derived schemes -- what we call the…

We construct the $\Lambda$-adic de Rham analogue of Hida's ordinary $\Lambda$-adic \'etale cohomology and of Ohta's $\Lambda$-adic Hodge cohomology, and by exploiting the geometry of integral models of modular curves over the cyclotomic…