Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Bruno Kahn, Hiroyasu Miyazaki, Shuji Saito, Takao Yamazaki

Abstract

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 has been developed.

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

Abstract

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 has been developed.

Paper Structure

This paper contains 31 sections, 57 theorems, 110 equations.

Table of Contents

  1. Review of presheaf theory on modulus pairs
  2. Categories of modulus pairs
  3. Presheaves
  4. Review of sheaf theory on non-proper modulus pairs
  5. The $\operatorname{\underline{MV}}^{\operatorname{fin}}$ cd-structure
  6. The $\operatorname{\underline{MV}}$ cd-structure
  7. A cd-structure on $\operatorname{\mathbf{MSm}}$
  8. Off-diagonal
  9. The $\operatorname{MV}$ cd-structure
  10. Sheaves on $\operatorname{\mathbf{MSm}}$ and $\operatorname{\mathbf{MCor}}$
  11. Sheaves on $\operatorname{\mathbf{MSm}}$
  12. Sheaves on $\operatorname{\mathbf{MCor}}$
  13. Cohomology in $\operatorname{\mathbf{MNST}}$
  14. Main result
  15. A generation lemma
  16. ...and 16 more sections

Key Result

Theorem \oldthetheorem

The following assertions hold.

Theorems & Definitions (113)

  • Definition 1
  • Definition 2
  • Theorem \oldthetheorem: kmsy
  • Definition 3
  • Theorem \oldthetheorem: see Lemmas \ref{['l4.2']} and \ref{['lem:tau!-exact']}, Theorems \ref{['thm:a-nis-final']}, \ref{['thm;tauexact']} and \ref{['thm:coh-MNST']}
  • Theorem \oldthetheorem: see Proposition \ref{['prop:MNST-NST']} and Theorem \ref{['prop:MNST-NST-coh']}
  • Definition 1.2.1
  • Lemma 1.2.3: kmsy
  • Lemma 1.2.4: kmsy
  • Lemma 1.2.5: kmsy
  • ...and 103 more