We construct the\'etale motivic Borel-Moore homology of derived Artin stacks. Using a
derived version of the intrinsic normal cone, we construct fundamental classes of quasi …

We prove that the∞-category of MGL-modules over any scheme is equivalent to the∞-
category of motivic spectra with finite syntomic transfers. Using the recognition principle for …

Let $ A=(a_1,\ldots, a_n) $ be a vector of integers with $ d=\sum_ {i= 1}^ n a_i $. By partial
resolution of the classical Abel-Jacobi map, we construct a universal twisted double …

We prove a recognition principle for motivic infinite P1-loop spaces over a perfect field. This
is achieved by developing a theory of framed motivic spaces, which is a motivic analogue of …

Using the motivic stable homotopy category over a field k, a smooth variety X over k has an
Euler characteristic χ (X/k) in the Grothendieck-Witt ring GW (k). The rank of χ (X/k) is the …

We extend the stable motivic homotopy category of Voevodsky to the class of scalloped
algebraic stacks, and show that it admits the formalism of Grothendieck's six operations …

In this paper we consider three types of localization theorems for algebraic stacks:(i)
Concentration, or cohomological localization. Given an algebraic group acting on a scheme …

The aim of this paper is to construct the cohomological Hall algebras for $3 $-Calabi--Yau
categories admitting a strong orientation data. This can be regarded as a mathematical …

We prove a topological invariance statement for the Morel–Voevodsky motivic homotopy
category up to inverting exponential characteristics of residue fields. This implies in …

We show that curve enumeration invariants of complex threefolds with nef anti-canonical
bundle are determined by their values on local curves. This statement and its proof are …