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June 19, 2026Forum of Mathematics SigmaOpen Access

Co-rank 1 11 Arithmetic Siegel–Weil IV: Analytic local-to-global

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Authors

RCRyan Chen

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Overview

Proves the arithmetic Siegel-Weil formula for cycles in unitary Shimura varieties, highlighting key local values.

Key Points

  • To establish the arithmetic Siegel-Weil formula in co-rank 1 for special cycles in unitary Shimura varieties.
  • Developed precise normalizations for Siegel Eisenstein series
  • Proved local Siegel-Weil special value formulas
  • Used geometric results for complex 0-cycles to finalize proofs.
  • Confirmed encoding of Kudla–Rapoport special 1-cycles in first derivatives of Eisenstein series Fourier coefficients.
  • Provided explicit constants for local Siegel-Weil formulas.
  • Completed the proof of the arithmetic Siegel–Weil results by integrating local theorems from previous papers.

Cite This Study

Ryan Chen (2026) studied this question.

synapsesocial.com/papers/6a34dff765a5b0777af2ef96https://doi.org/10.1017/fms.2026.10231
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