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On Deligne's conjecture for Hecke characters

Yubo Jin, Dongwen Liu, Binyong Sun

Abstract

This paper provides a proof of Deligne's conjecture for critical values of Hecke L-functions following a strategy originated by Harder and Schappacher.

On Deligne's conjecture for Hecke characters

Abstract

This paper provides a proof of Deligne's conjecture for critical values of Hecke L-functions following a strategy originated by Harder and Schappacher.

Paper Structure

This paper contains 18 sections, 10 theorems, 177 equations.

Table of Contents

  1. Introduction
  2. Algebraic Hecke characters and periods
  3. Algebraic Hecke characters
  4. Periods associated to algebraic Hecke characters
  5. The toroidal integral
  6. The Eisenstein series
  7. The global integral
  8. The local integral
  9. The archimedean modular symbols
  10. Lie algebras, measures, and orientations
  11. Finite-dimensional representations
  12. Cohomology for degenerate principal series representations
  13. The archimedean modular symbols
  14. Modular symbols and Hecke L-values
  15. $\mathrm{Aut}(\mathbb{C})$-action on coefficient systems
  16. ...and 3 more sections

Key Result

Theorem 2

Let $\chi$ be a critical algebraic Hecke character of a number field ${\mathrm {K}}$ with values in a number field ${\mathrm {E}}$. Assume that ${\mathrm {K}}$ contains a CM field and let $\mathrm k$ be the maximal CM subfield of ${\mathrm {K}}$. Set $\check{\chi}:=\chi|_{\mathbb A_\mathrm k^\times}

Theorems & Definitions (17)

  • Conjecture 1
  • Theorem 2
  • Proposition 3
  • Theorem 4
  • Lemma 5
  • proof
  • Lemma 6
  • Lemma 7
  • proof
  • Lemma 8
  • ...and 7 more