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

  title={A motivic homotopy theory without \$\$\mathbb \{A\}^\{1\}\$\$-invariance},
  author={Federico Binda},
  journal={Mathematische Zeitschrift},
  • F. Binda
  • Published 5 September 2019
  • Mathematics
  • Mathematische Zeitschrift
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. 

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