# Generating series of a new class of orthogonal Shimura varieties

## TL;DR

This paper introduces a new class of orthogonal Shimura varieties over totally real fields, constructs special cycles on them, and proves the modularity of their generating series in cohomology.

## Contribution

It develops a novel class of Shimura varieties, constructs associated special cycles, and establishes the modularity of their generating series, advancing understanding in arithmetic geometry.

## Key findings

- Construction of new orthogonal Shimura varieties over totally real fields
- Definition of special cycles on these varieties
- Proof of modularity of Kudla's generating series in cohomology

## Abstract

For a new class of Shimura varieties of orthogonal type over a totally real number field, we construct special cycles and show the the modularity of Kudla's generating series in the cohomology group.