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 (P1,∞)-local complexes of sheaves with log transfers. The homotopy t-structure on logDMeff(k) is proved to be compatible with Voevodsky’s t-structure; that is, we show that the comparison functor R□¯¯¯¯ω∗:DMeff(k)→logDMeff(k) is t-exact. The heart of the homotopy t-structure on logDMeff(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.
Connectivity and purity for logarithmic motives / F. Binda, A. Merici. - In: JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU. - ISSN 1474-7480. - (2021 Jun 14). [Epub ahead of print]
Titolo: | Connectivity and purity for logarithmic motives | |
Autori: | ||
Parole Chiave: | motives; logarithmic schemes; cohomology theories | |
Settore Scientifico Disciplinare: | Settore MAT/03 - Geometria | |
Progetto: | Geometric, algebraic and analytic methods in arithmetic | |
Data di pubblicazione: | 14-giu-2021 | |
Rivista: | ||
Tipologia: | Article (author) | |
Data ahead of print / Data di stampa: | 14-giu-2021 | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1017/S1474748021000256 | |
Appare nelle tipologie: | 01 - Articolo su periodico |
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File | Descrizione | Tipologia | Licenza | |
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connectivity-JIMJ.pdf | Post-print, accepted manuscript ecc. (versione accettata dall'editore) | Open Access Visualizza/Apri | ||
Jussieu-final-connectivity.pdf | Publisher's version/PDF | Open Access Visualizza/Apri |