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Connectivity of the slice filtration

  • Dipankar Maity
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Abstract

Using methods similar to Morel's stable connectivity theorem, we prove that, over an arbitrary field, the Tate truncation functors f0/n preserve motivic connectivity of $ S^1$-spectra. An analogous result for complexes yields a Hurewicz theorem for the Lp,n- and Lbirn-localizations over perfect fields. Over such fields, we establish a stronger connectivity property for categories of correspondences, showing that fnC preserves connectivity of motivic spectra with π’ž-transfers, whenever π’ž satisfies cancellation. We then use the motivic reconstruction theorem to deduce that fn, and consequently sn and f0/n, also preserve connectivity for effective (and thereby, β„™1-) motivic spectra. Along the way, we also establish the slice analog of the motivic (effective) reconstruction theorem, as well as the slice analog of motivic S1- and β„™1-recognition theorems.

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Cite

BibTeXRIS
BibTeX
@misc{maity2026connectivity,
  title = {{Connectivity of the slice filtration}},
  author = {Dipankar Maity},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.34535},
  eprint = {2609.34535},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05768406v1},
}
RIS
TY  - UNPB
TI  - Connectivity of the slice filtration
AU  - Dipankar Maity
PY  - 2026
DA  - 2026/09/28
PB  - HAL
DO  - 10.48550/arxiv.2609.34535
UR  - https://hal.science/hal-05768406v1
AB  - Using methods similar to Morel's stable connectivity theorem, we prove that, over an arbitrary field, the Tate truncation functors f_0/n preserve motivic connectivity of $ S^1$-spectra. An analogous result for complexes yields a Hurewicz theorem for the L^p,n- and L_bir^n-localizations over perfect fields. Over such fields, we establish a stronger connectivity property for categories of correspondences, showing that f_n^C preserves connectivity of motivic spectra with π’ž-transfers, whenever π’ž satisfies cancellation. We then use the motivic reconstruction theorem to deduce that f_n, and consequently s_n and f_0/n, also preserve connectivity for effective (and thereby, β„™^1-) motivic spectra. Along the way, we also establish the slice analog of the motivic (effective) reconstruction theorem, as well as the slice analog of motivic S^1- and β„™^1-recognition theorems.
ER  -