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TOPOLOGIES ON SCHEMES AND MODULUS PAIRS

Part of: $K$-theory in number theory (Co)homology theory $K$-theory in geometry Higher algebraic $K$-theory

Published online by Cambridge University Press:  13 July 2020

BRUNO KAHN Open the ORCID record for BRUNO KAHN [Opens in a new window]  and
HIROYASU MIYAZAKI Open the ORCID record for HIROYASU MIYAZAKI [Opens in a new window]
BRUNO KAHN
Affiliation:
IMJ-PRG, Case 247, 4 place Jussieu, 75252 Paris Cedex 05, France email bruno.kahn@imj-prg.fr
HIROYASU MIYAZAKI
Affiliation:
RIKEN iTHEMS, Wako, Saitama351-0198, Japan email hiroyasu.miyazaki@riken.jp
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Abstract

We study relationships between the Nisnevich topology on smooth schemes and certain Grothendieck topologies on proper and not necessarily proper modulus pairs, which were introduced in previous papers. Our results play an important role in the theory of sheaves with transfers on proper modulus pairs.

MSC classification

Primary: 19E15: Algebraic cycles and motivic cohomology
Secondary: 14F42: Motivic cohomology; motivic homotopy theory 19D45: Higher symbols, Milnor $K$-theory 19F15: Symbols and arithmetic
Type
Article
Information
Nagoya Mathematical Journal , Volume 244 , December 2021 , pp. 283 - 313
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Copyright
© 2020 Foundation Nagoya Mathematical Journal

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Footnotes

The first author acknowledges the support of Agence Nationale de la Recherche (ANR) under reference ANR-12-BL01-0005. The work of the second author is supported by Fondation Sciences Mathématiques de Paris (FSMP), RIKEN Special Postdoctoral Researchers (SPDR) Program, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), and JSPS KAKENHI Grant (19K23413).

References

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Acronyms

Grothendieck, A. and Dieudonné, J., Éléments de goémétrie algébrique: IV. Étude locale des schémas et des morphismes de schémas, Quatrième partie , Publ. Math. Inst Hautes Études Sci. 32 (1967), 5–361.Google Scholar
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