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

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.Contents 1. Introduction 2. Preliminaries 3. Functoriality on the flag variety 4. Pullbacks on adic Shimura varieties 5. Locally analytic cohomology 6. Families of cohomology classes 7. Families of anticyclotomic characters 8. Construction of the p-adic L-function Appendix A. Branching laws Appendix B. Comparisons in families Appendix C. Unitary base change References