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On the p-adic interpolation of unitary Friedberg--Jacquet periods

Andrew Graham

Abstract

We establish functoriality of higher Coleman theory for certain unitary Shimura varieties and use this to construct a $p$-adic analytic function interpolating unitary Friedberg--Jacquet periods.

On the p-adic interpolation of unitary Friedberg--Jacquet periods

Abstract

We establish functoriality of higher Coleman theory for certain unitary Shimura varieties and use this to construct a -adic analytic function interpolating unitary Friedberg--Jacquet periods.

Paper Structure

This paper contains 50 sections, 53 theorems, 217 equations.

Table of Contents

  1. Introduction
  2. Unitary Friedberg--Jacquet periods
  3. Statement of the results
  4. Notation
  5. Acknowledgements
  6. Preliminaries
  7. Shimura varieties
  8. Automorphic vector bundles
  9. Discrete series representations
  10. Some important elements
  11. Level subgroups at p
  12. Branching laws
  13. Functoriality on the flag variety
  14. The Bruhat stratification
  15. Tubes in the flag variety
  16. ...and 35 more sections

Key Result

Theorem 2

There exists a Zariski dense subset of classical weights $\Sigma^{\mathrm{int}} \subset U \times \mathcal{W}_H$ and a $p$-adic analytic function $\mathscr{L}_p = \mathscr{L}_p(\underline{\eta}. \underline{\chi}) \in \mathcal{O}(U \times \mathcal{W}_H)$ which interpolates the periods $\mathscr{P}_{\u

Theorems & Definitions (177)

  • Conjecture 1
  • Remark 1.1.2
  • Theorem 2: Corollary \ref{['RelationToAutoPeriods']}
  • Corollary 3
  • Remark 1.1.3
  • Remark 1.1.4: Example \ref{['BorelImpliesSSExample']}
  • Remark 1.1.5
  • Definition 2.0.1
  • Remark 2.0.2
  • Definition 2.0.3
  • ...and 167 more