Related papers: Foundations of Logarithmic Adic Spaces
The purpose of this article is to relate coarse cohomology of metric spaces with a more computable cohomology. We introduce a notion of boundedly supported cohomology and prove that coarse cohomology of many spaces are isomorphic to the…
We study affine maps between CAT(0) spaces with geometric actions, and show that they essentially split as products of dilations and linear maps (on the Euclidean factor). This extends known results from the Riemannian case. Furthermore, we…
We give an introduction to logic tailored for algebraists, explaining how proofs in linear logic can be viewed as algorithms for constructing morphisms in symmetric closed monoidal categories with additional structure. This is made explicit…
The mod p cohomology of a space comes with an action of the Steenrod Algebra. L. Schwartz [A propos de la conjecture de non realisation due a N. Kuhn, Invent. Math. 134, No 1, (1998) 211--227] proved a conjecture due to N. Kuhn [On…
$p$-Adic compactifications of geometric loop and diffeomorphism groups of compact manifolds on finite-dimensional spaces over non-Archimedean fields are investigated. Weakened topology is introduced. The structure of newly constructed…
In this paper, we study affine commutative algebraic monoid structures on affine spaces over an arbitrary field of characteristic zero. We obtain full classification of such structures on $\mathbb{A}_K^2$ and $\mathbb{A}_K^3$ and describe…
We develop a general theory of log spaces, in which one can make sense of the basic notions of logarithmic geometry, in the sense of Fontaine-Illusie-Kato. Many of our general constructions with log spaces are new, even in the algebraic…
We prove \cite[Conjecture~5.17]{Clausen} on the local light--profinite structure of smooth $p$-adic analytic Artin stacks. The argument proceeds in several reductions. First, by proving a generalization of van~Dantzig theorem for groupoids,…
A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…
We develop a theory of \emph{locally Frobenius algebras} which are colimits of certain directed systems of Frobenius algebras. A major goal is to obtain analogues of the work of Moore \& Peterson and Margolis on \emph{nearly Frobenius…
This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In three previous papers, we introduce the notion of formal manifolds and study…
The characteristic feature of the adeles is that they involve localizations of products (or equivalently restricted products of localizations). The point of this paper is to introduce an adelic style cohomological invariant of a partially…
We complete the classification of algebraic monoid structures on the affine 3-space. The result is based on a reduction of the general case to that of commutative monoids. We also study various algebraic properties of all monoids appearing…
We study three different topologies on the moduli space $\mathscr{H}^{\rm loc}_m$ of equivariant isometry classes of $m$-dimensional locally homogeneous Riemannian spaces. As an application, we provide the first examples of locally…
These lecture notes are based on the second course in a series of lectures at the Spring school "Non-archimedean geometry and Eigenvarieties" in March 2023 in Heidelberg. The objective of the first three courses was to give an introduction…
We study representations of the Loop Kac-Moody Lie algebra g \otimes A, where g is any Kac-Moody algebra and A is a ring of Laurent polynomials in n commuting variables. In particular, we study representations with finite dimensional weight…
We define and study infinite root stacks of fine and saturated logarithmic schemes, a limit version of the root stacks introduced by Niels Borne and the second author. We show in particular that the infinite root stack determines the…
Unstable operations in a generalized cohomology theory E give rise to a functor from the category of algebras over E to itself which is a colimit of representable functors and a comonoid with respect to composition of such functors. In this…
We construct a logarithmic version of the Hilbert scheme, and more generally the Quot scheme, of a simple normal crossings pair. The logarithmic Quot space admits a natural tropicalisation called the space of tropical supports, which is a…
The paper provides a combinatorial method to decide when the space of local systems with non vanishing first cohomology on the complement to an arrangement of lines in a complex projective plane has as an irreducible component a subgroup of…