In this paper, we continue the program initiated by Kahn–Saito–Yamazaki by constructing and studying an unstable motivic homotopy category with modulus MH(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 A1-invariant generalized cohomology theories.
A motivic homotopy theory without A1-invariance / F. Binda. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - (2019). [Epub ahead of print] [10.1007/s00209-019-02399-2]
A motivic homotopy theory without A1-invariance
F. Binda
2019
Abstract
In this paper, we continue the program initiated by Kahn–Saito–Yamazaki by constructing and studying an unstable motivic homotopy category with modulus MH(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 A1-invariant generalized cohomology theories.
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