相关论文: Integral Artin motives I: Smooth objects and the o…

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,…

We calculate the total derived functor for the map from the Weil-etale site introduced by Lichtenbaum to the etale site for varieties over finite fields. In particular, there is a long exact sequence relating Weil-etale cohomology and etale…

To any dg-category $T$ (over some base ring $k$), we define a $D^{-}$-stack $\mathcal{M}_{T}$ in the sense of \cite{hagII}, classifying certain $T^{op}$-dg-modules. When $T$ is saturated, $\mathcal{M}_{T}$ classifies compact objects in the…

For every stable model category $\mathcal{M}$ with a certain extra structure, we produce an associated model structure on the pro-category pro-$\mathcal{M}$ and a spectral sequence, analogous to the Atiyah-Hirzebruch spectral sequence, with…

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…

This work brings Mellin transforms into the realm of motivic integration. The new, larger class of motivic functions is stable under motivic Mellin and Fourier transforms, with general Fubini results and change of variables formulas. It…

In the present article we define an integral analogue of Chow-K\"unneth decomposition for \'etale motives. By using families of conservative functors we are able to establish a decomposition of the \'etale motive of commutative group…

Anderson t-modules are analogs of abelian varieties in positive characteristic. Associated to such a t-module, there are its t-motive and its dual t-motive. When dealing with these objects, several questions occur which one would like to…

This is a survey on Anderson t-motives -- high-dimensional generalizations of Drinfeld modules. They are the functional field analogs of abelian varieties with multiplication by an imaginary quadratic field. We describe their lattices,…

The aim of this work is to construct certain homotopy t-structures on various categories of motivic homotopy theory, extending works of Voevodsky, Morel, D\'eglise and Ayoub. We prove these $t$-structures possess many good properties, some…

We give a new construction, based on categorical logic, of Nori's $\mathbb Q$-linear abelian category of mixed motives associated to a cohomology or homology functor with values in finite-dimensional vector spaces over $\mathbb Q$. This new…

Consider a finite-dimensional real vector space equipped with a finite group acting unitarily on it. We address the general problem of constructing Euclidean stable embeddings of the quotient space of orbits. Our approach is based on…

Inspired by the work of G. Harder (\cite{HaICM}, \cite{HaLNM}, \cite{HaMM}) we construct via the motive of a Hilbert modular surface an extension of a Tate motive by a Dirichlet motive. We compute the realisation classes and indicate how…

We introduce in this work the notion of the category of pure $\mathbf{E}$-Motives, where $\mathbf{E}$ is a motivic strict ring spectrum and construct twisted $\mathbf{E}$-cohomology by using six functors formalism of J. Ayoub. In…

In this paper we study the Cartan matrix associated to the Ext-projective stratifying system induced by a basic and $\tau$-rigid object $M$ in mod$(A)$ by means of the $g$-vectors of the indecomposable direct summands of $M$. In particular…

We present a decomposition of the space of twisted arcs of a toric stack. As a consequence, we give a combinatorial description of the motivic integral associated to a torus-invariant divisor of a toric stack.

The main objective of this article is to establish the $p$-adic Artin formalism for the algebraic $p$-adic $L$-functions attached to the adjoint representations of Coleman families of modular forms. In particular, we prove a factorization…

We compute Benois $\mathscr{L}$-invariants of weight $1$ cuspforms and of their adjoint representations and show how this extends Gross' $p$-adic regulator to Artin motives which are not critical in the sense of Deligne. Benois'…

We show in many cases the existence of adjoints to extension of scalars on categories of motivic nature, in the framework of field extensions. This is to be contrasted with the more classical situation where one deals with a finite type…

We show that the derived category of perverse Nori motives and mixed Hodge modules are the derived categories of their constructible hearts. This enables us to construct $\infty$-categorical lifts of the six operations and therefore to…