Related papers: A general formalism for logarithmic structures
We show that certain spaces of log-integrable functions and operators are complete topological *-algebras with respect to a natural metric space structure. We explore connections with the Nevanlinna class of holomorphic functions.
We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…
This paper is about a correspondence between monoidal structures in categories and $n$-fold loop spaces. We develop a new syntactical technique whose role is to substitute the coherence results, which were the main ingredients in the proofs…
We develop some concrete methods to build Sarkisov links, starting from Mori fibre spaces. This is done by studying low rank Cox rings and their properties. As part of this development, we give an algorithm to construct explicitly the…
We set up a formalism of Maurer-Cartan moduli sets for L-infinity algebras and associated twistings based on the closed model category structure on formal differential graded algebras (a.k.a. differential graded coalgebras). Among other…
These notes present an approach to obtaining monoid operations which are compatible with a given family of mappings in the sense that the mappings become left translations in the monoid. This can be applied to various situations such as the…
Given a morphism $X \to S$ of fine log schemes, we develop a geometric description of the sheaves of higher-order differentials $\Omega^n_{X/S}$ for $n > 1$, as well as a definition of the de Rham complex in terms of this description.
We introduce the notion of strong regular embeddings of Deligne-Mumford stacks. These morphisms naturally arise in the related contexts of generalized Euler sequences and hypertoric geometry.
This is a survey on formality results relying on weight structures. A weight structure is a naturally occurring grading on certain differential graded algebras. If this weight satisfies a purity property, one can deduce formality. Algebraic…
Using log-geometry, we construct a model for the configuration category of a smooth algebraic variety. As an application, we prove the formality of certain configuration spaces.
We introduce torsoids, a canonical structure in matching covered graphs, corresponding to the bricks and braces of the graph. This allows a more fine-grained understanding of the structure of finite and infinite directed graphs with respect…
This paper concerns arithmetic families of $\varphi$-modules over reduced affinoid spaces. For such a family, we first prove that the slope polygons is lower semicontinuous around any rigid point. If the slope polygons are locally constant…
This paper is the sequel to [PTVV] (IHES Vol. 117, 2013). We develop a general and flexible context for differential calculus in derived geometry, including the de Rham algebra and polyvector fields. We then introduce the formalism of…
We impose a rather unknown algebraic structure called a `hyperstructure' to the underlying space of an affine algebraic group scheme. This algebraic structure generalizes the classical group structure and is canonically defined by the…
The local structure of a tiling is described in terms of a multiplicative structure on its pattern classes. The groupoid associated to the tiling is derived from this structure and its integer group of coinvariants is defined. This group…
This is an expended and revised version of the preprint "Schematization of homotopy types". The purpose of this work is to introduce a notion of \emph{affine stacks}, which is a homotopy version of the notion of affine schemes, and to give…
We generalize the constructions of [17,19] to layered semirings, in order to enrich the structure and provide finite examples for applications in arithmetic (including finite examples). The layered category theory of [19] is extended…
A shelf is a set with a binary operation~$\op$ satisfying $a \op (b \op c) = (a \op b) \op (a \op c)$. Racks are shelves with invertible translations $b \mapsto a \op b$; many of their aspects, including cohomological, are better understood…
We explain a formalism of regular holonomic $D$-modules for algebraic geometers using the distinguished triangles associated with algebraic local cohomology together with meromorphic Deligne extensions of local systems as well as the dual…
The space of codimension one holomorphic foliations of degree 1 in a projective space has an irreducible component whose general element is a logarithmic differential 1-form with simple poles in three hyperplanes. We compute its projective…