Cancellation theorems for reciprocity sheaves

Merici, Alberto; Saito, Shuji

doi:10.14231/ag-2023-005

Cited by 1 publication

(1 citation statement)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [27,. See [27] and [23] for some computations. In particular, a nontrivial argument (see [27,Theorem 5.2]) shows that (F,G) RSCNis = F ⊗ HINis G whenever F,G ∈ HI Nis and ch(k) = 0.…”

Section: Application To Reciprocity Sheavesmentioning

confidence: 99%

Connectivity and Purity for Logarithmic Motives

Binda¹,

Merici²

2021

J. Inst. Math. Jussieu

View full text Add to dashboard Cite

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-structure; that is, we show that the comparison functor $R^{{\overline {\square }}}\omega ^*\colon {\operatorname {\mathbf {DM}^{eff}}}(k)\to {\operatorname {\mathbf {logDM}^{eff}}}(k)$ is t-exact. The heart of the homotopy t-structure on ${\operatorname {\mathbf {logDM}^{eff}}}(k)$ is the Grothendieck abelian category of strictly cube-invariant sheaves with log transfers: we use it to build a new version of the category of reciprocity sheaves in the style of Kahn-Saito-Yamazaki and Rülling.

show abstract