Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Some comments on my study of period-integrals

Daniel Barlet

Abstract

This text is a presentation (without proofs) of some of my recent results on the singular terms of asymptotic expansions of period-integrals using (a,b)-modules. I try to explain why this simple algebraic structure is interesting and useful.

Some comments on my study of period-integrals

Abstract

This text is a presentation (without proofs) of some of my recent results on the singular terms of asymptotic expansions of period-integrals using (a,b)-modules. I try to explain why this simple algebraic structure is interesting and useful.
Paper Structure (11 sections, 8 theorems, 21 equations)

This paper contains 11 sections, 8 theorems, 21 equations.

Table of Contents

  1. Abstract.
  2. AMS classification.
  3. Key words.
  4. Introduction
  5. The context
  6. (a,b)-modules and asymptotic expansions
  7. Notation.
  8. Example.
  9. The use of frescos
  10. Semi-simple filtration and Higher Bernstein polynomials
  11. Bibliography

Key Result

Theorem 3.0.7

Any geometric (a,b)-module $E$ admits an embedding as a sub-module of some $\Xi_{\mathscr{A}}^{(N)} \otimes_{\mathop{\mathrm{\mathbb{C}}}\nolimits} V$. Moreover we may choose $\mathscr{A}$ as the image in $\mathbb{Q}/\mathbb{Z} \simeq ]0, 1] \cap \mathbb{Q}$ of the opposite of the roots of the Berns

Theorems & Definitions (18)

  • Definition 3.0.1
  • Definition 3.0.2
  • Definition 3.0.3
  • Definition 3.0.4
  • Definition 3.0.5
  • Definition 3.0.6
  • Theorem 3.0.7
  • Definition 4.0.1
  • Theorem 4.0.2
  • Theorem 4.0.3
  • ...and 8 more