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The Fontaine-Ogus realisation of Laumon 1-motives

Nicola Mazzari

Abstract

We construct the (filtered) Ogus realisation of Laumon 1-motives over a number field. This realisation extends the functor defined on Deligne 1-motives by Andreatta, Barbieri-Viale and Bertapelle.

The Fontaine-Ogus realisation of Laumon 1-motives

Abstract

We construct the (filtered) Ogus realisation of Laumon 1-motives over a number field. This realisation extends the functor defined on Deligne 1-motives by Andreatta, Barbieri-Viale and Bertapelle.

Paper Structure

This paper contains 10 sections, 8 theorems, 23 equations.

Table of Contents

  1. Introduction
  2. 1-motives
  3. Laumon 1-motives
  4. Morphisms
  5. Devissage of Laumon 1-motives
  6. Adding the Hodge filtration
  7. $p$-adic Hodge theory for 1-motives
  8. Fontaine--Ogus modules
  9. Extending the realisation to Laumon 1-motives
  10. The target category

Key Result

Theorem 1.1

There exists a is fully faithful realisation functor extending $T_{\mathbf{FOg}}$.

Theorems & Definitions (24)

  • Theorem 1.1
  • Remark 2.1
  • Remark 2.2
  • Proposition 2.3
  • proof
  • Proposition 2.4
  • proof
  • Remark 2.5
  • Corollary 2.6
  • proof
  • ...and 14 more