# A motivic homotopy theory without $$\mathbb {A}^{1}$$-invariance

@article{Binda2019AMH, title={A motivic homotopy theory without \$\$\mathbb \{A\}^\{1\}\$\$-invariance}, author={Federico Binda}, journal={Mathematische Zeitschrift}, year={2019} }

In this paper, we continue the program initiated by Kahn–Saito–Yamazaki by constructing and studying an unstable motivic homotopy category with modulus \(\overline{\mathbf{M}}\mathcal {H}(k)\), extending the Morel–Voevodsky construction from smooth schemes over a field k to certain diagrams of schemes. We present this category as a candidate environment for studying representability problems for non \(\mathbb {A}^1\)-invariant generalized cohomology theories.

## 2 Citations

### Motives with modulus, III: The categories of motives

- Mathematics, Materials ScienceAnnals of K-Theory
- 2022

We construct and study a triangulated category of motives with modulus $\mathbf{MDM}_{\mathrm{gm}}^{\mathrm{eff}}$ over a field $k$ that extends Voevodsky's category…

### Cohomology of the moduli stack of algebraic vector bundles

- MathematicsAdvances in Mathematics
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