Related papers: Log motivic exceptional direct image functors

We define an $\infty$-category of rational motives for inverse limits of algebraic stacks, so-called pro-algebraic stacks. We show that it admits a $6$-functor formalism for certain classes of morphisms. On pro-schemes, we show that this…

For each fs log scheme $(X,\mathcal M_X)$ over a field $k$ we construct a geometrical Voevodsky motive $[X]^{log}\in DM_{gm}(k,\mathbb Q)$. We prove that, for $k=\mathbb C$, the Betti realization of $[X]^{log}$ is the log Betti cohomology…

In this paper, we generally describe a method of taking an abstract six functors formalism in the sense of Khan or Cisinski-D\'{e}glise, and outputting a derived motivic measure in the sense of Campbell-Wolfson-Zakharevich. In particular,…

We develop notions of integrable functions within the theory of schemic motivic integration.

Gluing of two pseudo functors has been studied by Deligne, Ayoub, and others in the construction of extraordinary direct image functors in \'etale cohomology, stable homotopy, and mixed motives of schemes. In this article, we study more…

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.

In this article, we study criteria for producing six-functor formalisms and morphisms between them. One notable application is that the motivic homotopy theory of algebraic stacks is the universal six-functor functor formalism in a strong…

We prove that arbitrary pullbacks, as well as Betti and \'etale realisation functors, are t-exact for the constructible motivic t-structure on the category of cohomological 1-motives over a base scheme.

For directed graph iterated function systems (IFSs) defined on R, we prove that a class of 2-vertex directed graph IFSs have attractors that cannot be the attractors of standard (1-vertex directed graph) IFSs, with or without separation…

We show exactness of the homotopy sequence for the logarithmic fundamental group in the case of log smooth, finitely presented, proper and saturated morphisms of fs log schemes over a field. This generalizes earlier results of Hoshi in the…

A theory of a derivator version of six-functor-formalisms is developed, using an extension of the notion of fibered multiderivator due to the author. Using the language of (op)fibrations of 2-multicategories this has (like a usual fibered…

We prove the functoriality for proper push-forward of the characteristic cycles of constructible complexes by morphisms of smooth projective schemes over a perfect field, under the assumption that the direct image of the singular support…

In this paper, we introduce the category of real isotropic motivic spectra, and show that the real realization functor from motivic spectra over $\mathbb{R}$ to classical spectra factors through it. We then describe its cellular subcategory…

In this paper, we present a general approach to establish motivic cohomology and build part of its six operations formalism. Applying this together with symplectic orientation on MW-motivic cohomology, we discuss the embedding theorem of…

This article is first in a series of papers where we reprove the statements in constructing the Enhanced Operation Map and the abstract six-functor formalism developed by Liu-Zheng. In this paper, we prove a theorem regarding constructing…

In earlier work (arXiv:0801.0261), we gave a definition of an abelian category of motivic (constructible) sheaves over a base in characteristic zero using Nori's method. This category has Hodge and etale realizations, and is stable under…

This paper contains four main results associated with an attractor of a projective iterated function system (IFS). The first theorem characterizes when a projective IFS has an attractor which avoids a hyperplane. The second theorem…

For any polynomial f with complex coefficients we find a remarkable subset of poles of the motivic zeta function. It is combinatorially determined by any log resolution and it admits an intrinsic interpretation in terms of contact loci of…

We construct a perfect version of Morel--Voevodsky's motivic homotopy category over a perfect base scheme in positive characteristic. By checking the axioms of a coefficient system, we establish a six-functor formalism. We show that…

The aim of this article is to develop the theory of motivic integration over Deligne-Mumford stacks and to apply it to the birational geometry of stacks.