CONNECTIVITY AND PURITY FOR LOGARITHMIC MOTIVES

@article{Binda2021CONNECTIVITYAP,
  title={CONNECTIVITY AND PURITY FOR LOGARITHMIC MOTIVES},
  author={Federico Binda and Alberto Merici},
  journal={Journal of the Institute of Mathematics of Jussieu},
  year={2021}
}
  • F. BindaAlberto Merici
  • Published 15 December 2020
  • Mathematics
  • Journal of the Institute of Mathematics of Jussieu
The goal of this article is to extend the work of Voevodsky and Morel on the homotopy t-structure on the category of motivic complexes to the context of motives for logarithmic schemes. To do so, we prove an analogue of Morel’s connectivity theorem and show a purity statement for $({\mathbf {P}}^1, \infty )$ -local complexes of sheaves with log transfers. The homotopy t-structure on ${\operatorname {\mathbf {logDM}^{eff}}}(k)$ is proved to be compatible with Voevodsky’s t… 

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References

SHOWING 1-10 OF 41 REFERENCES

Reciprocity sheaves

We start developing a notion of reciprocity sheaves, generalizing Voevodsky’s homotopy invariant presheaves with transfers which were used in the construction of his triangulated categories of

Triangulated categories of logarithmic motives over a field

In this work we develop a theory of motives for logarithmic schemes over fields in the sense of Fontaine, Illusie, and Kato. Our construction is based on the notion of finite log correspondences, the

Tensor structures in the theory of modulus presheaves with transfers

The tensor product of $${\mathbb {A}}^1$$ A 1 -invariant sheaves with transfers introduced by Voevodsky is generalized to reciprocity sheaves via the theory of modulus presheaves with transfers. We

Purity of reciprocity sheaves

  • S. Saito
  • Mathematics
    Advances in Mathematics
  • 2020

T-model structures

For every stable model category M with a certain extra structure, we produce an associated model structure on the pro-category pro-M and a spectral sequence, analogous to the Atiyah-Hirzebruch

ERRATUM TO: CONNECTIVITY AND PURITY FOR LOGARITHMIC MOTIVES

The proof of [1, Lemma 7.2] contains a gap: the equality $\omega _{\sharp } h_{0}(\Lambda _{\mathrm {ltr}}(\eta ,\mathrm {triv})) = \omega _{\sharp } h_{0}(\omega ^{*}\Lambda _{\mathrm

Motives with modulus, III: The categories of motives

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

Cancellation theorems for reciprocity sheaves

We prove cancellation theorems for reciprocity sheaves and cube-invariant modulus sheaves with transfers of Kahn--Saito--Yamazaki, generalizing Voevodsky's cancellation theorem for

Motives with modulus, II: Modulus sheaves with transfers for proper modulus pairs

We develop a theory of sheaves and cohomology on the category of proper modulus pairs. This complements [KMSY21], where a theory of sheaves and cohomology on the category of non-proper modulus pairs