Related papers: The $\mathbf{P}^1$-motivic Gysin map

We construct the Gromov-Witten invariants of moduli of stable morphisms to $\Pf$ with fields. This is the all genus mathematical theory of the Guffin-Sharpe-Witten model, and is a modified twisted Gromov-Witten invariants of $\Pf$. These…

We develop a motivic framework for Feynman integrals of one-loop graphs in momentum space. Its advantage compared to the already existing framework in Feynman representation is that it naturally includes graphs with cuts. To each such…

Given a finite group G, we develop a theory of G-equivariant noncommutative motives. This theory provides a well-adapted framework for the study of G-schemes, Picard groups of schemes, G-algebras, 2-cocycles, equivariant algebraic K-theory,…

We construct a comparison functor between ($\mathbf{A}^1$-local) tame motives and ($\overline{\square}$-local) log-\'etale motives over a field $k$ of positive characteristic. This generalizes Binda--Park--{\O}stv{\ae}r's comparison for the…

We develop a renormalization theory of non-perturbative dissipative H\'enon-like maps with combinatorics of bounded type. The main novelty of our approach is the incorporation of Pesin theoretic ideas to the renormalization method, which…

This paper introduces the trivial fiber topology on schemes. For one-dimensional base schemes, we use it to describe fibrant replacements in the stable motivic homotopy category and motivic infinite loop spaces. We also extend the…

We consider piecewise expanding maps of the interval with finitely many branches of monotonicity and show that they are generically combinatorially stable, i.e., the number of ergodic attractors and their corresponding mixing periods do not…

Our goal is to prove that the Leray spectral sequence associated to a map of algebraic varieties is motivic in the following sense: If the singular cohomology groups of the category of quasiprojective varieties defined over a subfield of C…

We prove an unstable version of Morel's $\mathbb{A}^1$-connectivity theorem over arbitrary base schemes. In the stable setting, this recovers (and simplifies the proof of) the known connectivity bounds due to Morel, Schmidt--Strunk,…

In this article we study the normal bundle and the deformation to the normal cone functors to get deformation Lie groupoids that allow us to construct pushforward maps in any suitable (co)homology theory for Lie groupoids (not only…

We survey over some recent applications of motivic homotopy theory in the definition and the study of $p$-adic cohomology theories. In particular, we revisit the proof of the $p$-adic weight-monodromy conjecture for smooth projective…

Voevodsky outlined a conjectural programme that his slice filtration in motivic homotopy theory should give rise to a good theory of $\mathbb{A}^1$-invariant motivic cohomology. This paper achieves his vision in the generality of arbitrary…

We construct well-behaved extensions of the motivic spectra representing generalized motivic cohomology and connective Balmer--Witt K-theory (among others) to mixed characteristic Dedekind schemes on which 2 is invertible. As a consequence…

We prove the Gersten conjecture for $p$-adic \'etale Tate twists for a smooth scheme $X$ in mixed characteristic in the Nisnevich topology. Our main observation is that, while $p$-adic \'etale Tate twists are not $\mathbb A^1$-invariant,…

Over the past century, cohomology operations have played a crucial role in homotopy theory and its applications. A powerful framework for constructing such operations is the theory of commutative algebras in spectra. In this article, we…

We relate the group structure of van der Kallen on orbit sets of unimodular rows with values in a smooth algebra $A$ over a field $k$ with the motivic cohomotopy groups of the spectrum of $A$ with coefficients in $\mathbb{A}^n\setminus 0$…

As a higher dimensional version of the theory of Morse functions, there have been various studies of smooth manifolds using generic smooth maps. As fundamental results, in these studies, they have found that inverse images of such maps…

In this paper we prove C^k structure stability conjecture for unimodal maps. In other words, we shall prove that Action A maps are dense in the space of C^k unimodal maps in the C^k topology. Here k can be 1,2,...,\infty,\omega.

We study the statistical properties of piecewise expanding maps in the general setting of metric measure spaces. We provide sufficient conditions for exponential mixing of such systems with explicit estimates on the constants. We also…

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'…