Related papers: The relative GAGA Theorem and an application to th…
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. The main tool in our construction is the representability…
We prove some finiteness theorems for the Picard functor of an algebraic stack, in the spirit of SGA 6, exp. XII and XIII. In particular, we give a stacky version of Raynaud's relative representability theorem, we give sufficient conditions…
We develop an algebraic model for the relative sectional category of a continuous map in rational homotopy theory using commutative differential graded algebras (CDGAs). Our main result establishes that for formal maps, the rational…
We prove that every algebraic stack, locally of finite type over an algebraically closed field with affine stabilizers, is \'etale-locally a quotient stack in a neighborhood of a point with a linearly reductive stabilizer group. The proof…
Consider a Hamiltonian action of a compact connected Lie group $G$ on an aspherical symplectic manifold $(M,\omega)$. Under some assumptions on $(M,\omega)$ and the action, D. A. Salamon conjectured that counting gauge equivalence classes…
Let $\Gamma$ be a simplicial, finite, connected graph such that $\Gamma$ does not decompose as a nontrivial join. We prove that two notions of strong quasiconvexity and stability are equivalent in the right-angled Artin group $A_\Gamma$…
This is the integral text of my thesis. The first part is an expanded version of "Riemann-Roch theorems for Deligne-Mumford stacks", where I deal with Artin stacks over general bases. In the second part, I prove some Riemann-Roch statment…
The Perfect Graph Theorems are important results in graph theory describing the relationship between clique number $\omega(G) $ and chromatic number $\chi(G) $ of a graph $G$. A graph $G$ is called \emph{perfect} if $\chi(H)=\omega(H)$ for…
Recent work of An, Drummond-Cole, and Knudsen, as well as the author, has shown that the homology groups of configuration spaces of graphs can be equipped with the structure of a finitely generated graded module over a polynomial ring. In…
Derived de Rham cohomology has been recently used in several contexts, as in works of Beilinson and Bhatt on p-adic periods morphisms and Morin on numerical invariants for special values of zeta functions. Inspired by some results of Morin,…
We construct and study a graded version of absolute perfectoidization for $G$-graded adic rings. As a main geometric application, we show that the absolute perfectoidization of the structure sheaf of a projective-type formal scheme admits…
We classify torsion-free real-analytic affine connections on compact oriented real-analytic surfaces which are locally homogeneous on a nontrivial open set, without being locally homogeneous on all of the surface. In particular, we prove…
One fundamental consequence of a scheme $X$ being proper is that the functor classifying maps from $X$ to any other suitably nice scheme or algebraic stack is representable by an algebraic stack. This result has been generalized by…
Given a finite graph G there is a corresponding group given by the presentation with generators the vertices of G and a relation [x,y]=1 for generators x and y precisely when (x,y) is an edge of G. Such groups are known as partially…
We construct a relative Hodge-Tate spectral sequence for any smooth proper morphism of rigid analytic spaces over a perfectoid field extension of $\mathbb Q_p$. To this end, we generalise Scholze's strategy in the absolute case by using…
Let K be an algebraically closed field of characteristic zero, endowed with a complete nonarchimedean norm. Let X be a K-rigid analytic variety and \Sigma a semianalytic subset of X. Then the closure of \Sigma in X with respect to the…
Extending the Wedderburn-Artin theory of (classically) semisimple associative rings to the realm of topological rings with right linear topology, we show that the abelian category of left contramodules over such a ring is split…
We give a general criterion for conformal embeddings of vertex operator algebras associated to affine Lie algebras at arbitrary levels. Using that criterion, we construct new conformal embeddings at admissible rational and negative integer…
Perfect paradefinite algebras are De Morgan algebras expanded with an operation that allows for the full behavior of classical negation to be restored. They form a variety that is term-equivalent to the variety of involutive Stone algebras.…
We study graph products of groups from the viewpoint of measured group theory. We first establish a full measure equivalence classification of graph products of countably infinite groups over finite simple graphs with no transvection and no…