The zeroth stable homotopy groups of motivic spheres over the integers

@misc{rondigs2026zeroth,
  title = {{The zeroth stable homotopy groups of motivic spheres over the integers}},
  author = {Oliver Röndigs},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03069},
  eprint = {2610.03069},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03069},
}

TY  - UNPB
TI  - The zeroth stable homotopy groups of motivic spheres over the integers
AU  - Oliver Röndigs
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.03069
UR  - https://arxiv.org/abs/2610.03069
AB  - The main result determines the zeroth integral Milnor-Witt stem of the motivic sphere spectrum in the Morel-Voevodsky motivic stable homotopy category of the integers. The component in weight zero is the Grothendieck-Witt ring of nondegenerate symmetric bilinear forms over the integers. Along the way, cellularity of connective Witt theory, as well as an absolute purity result for the η-inverted motivic sphere spectrum, is established over Dedekind domains of mixed characteristic.
ER  -