Related papers: Rational Enriched Motivic Spaces
We define the notion of an enriched Reedy category, and show that if A is a C-Reedy category for some symmetric monoidal model category C and M is a C-model category, the category of C-functors and C-natural transformations from A to M is…
We prove the motivic classes in the motivic cohomology groups of Picard modular surfaces with non-trivial coefficients constructed in a paper of Loeffler\textendash Skinner\textendash Zerbes are in the motivic cohomology groups of the…
A mixed Weil cohomology with values in an abelian rigid tensor category is a cohomological functor on Voevodsky's category of motives which is satisfying K\"unneth formula and such that its restriction to Chow motives is a Weil cohomology.…
Magnitude homology is an invariant of enriched categories which generalizes ordinary categorical homology -- the homology of the classifying space of a small category. The classifying space can also be generalized in a different direction:…
We define a class of rational numbers including, as a particular case, the classical harmonic numbers. For one particular instance we apply it to the expansion into powers series of a special function, and also detail its relashionship with…
It is known that the so-called monadic decomposition, applied to the adjunction connecting the category of bialgebras to the category of vector spaces via the tensor and the primitive functors, returns the usual adjunction between…
Algebra and representation theory in modular tensor categories can be combined with tools from topological field theory to obtain a deeper understanding of rational conformal field theories in two dimensions: It allows us to establish the…
In this paper we determine the motivic class--in particular, the weight polynomial and conjecturally the Poincar\'e polynomial--of the open de Rham space, defined and studied by Boalch, of certain moduli spaces of irregular meromorphic…
We introduce a new notion of recursively generated enriched term which generalizes the one studied in joint work with Rosick\'y. These new terms come together with a notion of term-interpretability, which recovers the same type of…
The complete enriched Lie algebras constitue the natural extension of graded Lie algebras for connected spaces. Each complete enriched Lie algebra is the rational homotopy Lie algebra of a connected space. This text is the first part of a…
A functional equation for the motivic integral corresponding to the Milnor number of an arc is derived using the Denef-Loeser formula for the change of variables. Its solution is a function of five auxiliary parameters, it is unique up to…
For finite complex reflexion groups, we consider the graded $W$-modules of diagonally harmonic polynomials in $r$ sets of variables, and show that associated Hilbert series may be described in a global manner, independent of the value of…
We make some computations in stable motivic homotopy theory over Spec \mathbb{C}, completed at 2. Using homotopy fixed points and the algebraic K-theory spectrum, we construct a motivic analogue of the real K-theory spectrum KO. We also…
We present a categorical model for intuitionistic linear logic where objects are polynomial diagrams and morphisms are simulation diagrams. The multiplicative structure (tensor product and its adjoint) can be defined in any locally…
We introduce a subclass of linear recurrence sequences which we call poly-rational sequences because they are denoted by rational expressions closed under sum and product. We show that this class is robust by giving several…
We investigate connections between Lipschitz geometry of real algebraic varieties and properties of their arc spaces. For this purpose we develop motivic integration in the real algebraic set-up. We construct a motivic measure on the space…
We explore the possibility of extending Mardare et al. quantitative algebras to the structures which naturally emerge from Combinatory Logic and the lambda-calculus. First of all, we show that the framework is indeed applicable to those…
We propose a suitable substitute for the classical Grothendieck ring of an algebraically closed field, in which any quasi-projective scheme is represented, while maintaining its non-reduced structure. This yields a more subtle invariant,…
We compare the topological Milnor fibration and the motivic Milnor fibre of a regular complex function with only normal crossing singularities by introducing their common extension: the complete Milnor fibration. We give two equivalent…
We present some data on the cohomology of the motivic Steenrod algebra over an algebraically closed field. We discuss several features of the associated Adams spectral sequence, including the basic construction and convergence properties.…