Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Graded quotients of ramification groups of local fields with imperfect residue fields

Takeshi Saito

Abstract

We prove that the graded quotients of the filtration by ramification groups of any henselian discrete valuation field of residue characteristic $p>0$ are $F_p$-vector spaces. We define an injection of the character group of each graded quotient to a twisted cotangent space defined using a cotangent complex.

Graded quotients of ramification groups of local fields with imperfect residue fields

Abstract

We prove that the graded quotients of the filtration by ramification groups of any henselian discrete valuation field of residue characteristic are -vector spaces. We define an injection of the character group of each graded quotient to a twisted cotangent space defined using a cotangent complex.

Paper Structure

This paper contains 16 sections, 60 theorems, 92 equations.

Table of Contents

  1. Tangent spaces, immersions and differentials
  2. Tangent space at a point of a scheme
  3. Immersions to smooth schemes
  4. Differentials and conormal modules
  5. Smooth group schemes
  6. Additive torsors over vector spaces
  7. Étale isogenies of smooth group schemes
  8. Construction of functors
  9. Dilatations
  10. Normalizations
  11. Construction of functors
  12. Construction of an automorphism
  13. Ramification groups
  14. Ramification groups
  15. Reduction steps
  16. ...and 1 more sections

Key Result

Lemma 1.1.1

1. (Ill) Let $f\colon X\to Y$ be an immersion of schemes over a scheme $S$. Then, the boundary morphism $\partial\colon N_{X/Y}\to f^*\Omega^1_{Y/S}$ of the distinguished triangle $Lf^*L_{Y/S}\to L_{X/S}\to L_{X/Y} \to$ sends $g$ to $-dg$. 2. (Ill) Let $X\to S$ be a smooth morphism. Then, the canoni

Theorems & Definitions (70)

  • Lemma 1.1.1
  • Lemma 1.1.2
  • Proposition 1.1.3
  • Lemma 1.1.4
  • Proposition 1.1.5
  • Definition 1.1.6
  • Lemma 1.1.7
  • Proposition 1.1.8
  • Example 1.1.9
  • Proposition 1.1.10
  • ...and 60 more