Related papers: Some remarks on open analytic curves over non-arch…

It is now a classical result that an algebraic space locally of finite type over $\mathbf{C}$ is analytifiable if and only if it is locally separated. In this paper we study non-archimedean analytifications of algebraic spaces. We construct…

We construct a semi-stable formal model of a wide open rigid curve with a semi-stable covering, and study the l-adic cohomology of the rigid curve. We describe the l-adic cohomology of the rigid curve using the l-adic cohomology of the…

Let A be a finite abelian group. We set up an algebraic framework for studying A-equivariant complex-orientable cohomology theories in terms of a suitable kind of equivariant formal groups. We compute the equivariant cohomology of many…

We review the shape theory of $\infty$-topoi, and relate it with the usual cohomology of locally constant sheaves. Additionally, a new localization of profinite spaces is defined which allows us to extend the \'etale realization functor of…

This informal note collects key results and open problems on the (co)homology of the Deligne-Mumford moduli spaces of real marked rational curves. The open problems are both of topological nature, aiming to investigate the (co)homology of…

We compare flat cohomology with crystalline syntomic complexes in two cases: 1) $p$-divisible groups over a separated $\mathbb F_p$-scheme with local finite $p$-bases, 2) semi-abelian schemes over a separated irreducible smooth curve.

Cohomologies of nonassociative metagroup algebras are investigated. Extensions of metagroup algebras are studied. Examples are given.

In this paper, we first recall the notion of (noncommutative) Poisson conformal algebras and describe some constructions of them. Then we study the formal distribution (noncommutative) Poisson algebras and coefficient (noncommutative)…

We discuss the structure of integral etale motivic cohomology groups of smooth and projective schemes over algebraically closed fields, finite fields, local fields, and arithmetic schemes.

This article, addressed to a general audience of functional analysts, is intended to be an illustration of a few basic principles from `noncommutative functional analysis', more specifically the new field of {\em operator spaces.} In our…

We study some formality criteria for differential graded algebras over differential graded operads. This unifies and generalizes other known approaches like the ones by Manetti and Kaledin. In particular, we construct general operadic…

We prove several criteria for quasi-isometry between non-locally-finite graphs and their structure trees. Results of M\"oller in \cite{moeller92ends2} for locally finite and transitive graphs are generalized. We also give a criterion which…

In this investigation, we introduce the class of non-archimedean frames in spirit with the topological notion of non-archimedean spaces. We explore various properties of these frames - particularly their spaciality. We attach a base that…

We establish several compatibility results between residue maps in \'etale and Galois cohomology that arise naturally in the analysis of smooth affine algebraic curves having good reduction over discretely valued fields. These results are…

Let $X$ be a smooth quasi-projective surface over a number field $K$, and let $L$ be a foliation on $X$. We prove that if $L$ is closed under $p$-th powers for almost all primes $p$, then any $L$-invariant smooth formal curve is…

We study moduli of semistable twisted sheaves on smooth proper morphisms of algebraic spaces. In the case of a relative curve or surface, we prove results on the structure of these spaces. For curves, they are essentially isomorphic to…

We continue our study on infinitesimal lifting properties of maps between locally noetherian formal schemes started in math.AG/0604241. In this paper, we focus on some properties which arise specifically in the formal context. In this vein,…

In this paper, we extend a theorem of To\"en and Vaqui\'e to the non-Archimedean and formal settings. More precisely, we prove that a smooth and proper rigid analytic variety is algebraizable if and only if its category of perfect complexes…

We survey our works on the locally analytic vectors of completed cohomology of modular curves.

The classification, both up to isomorphism or up to equivalence, of the gradings on a finite dimensional nonassociative algebra A over an algebraically closed field F, such that its group scheme of automorphisms is smooth, is shown to be…