Theta cycles and the Beilinson–Bloch–Kato conjectures

Research output: Contribution to journalArticlepeer-review


We introduce ‘canonical’ classes in the Selmer groups of certain Galois representations with a conjugate-symplectic symmetry. They are images of special cycles in unitary Shimura varieties, and defined uniquely up to a scalar. The construction is a slight refinement of one of Y. Liu, based on the conjectural modularity of Kudla's theta series of special cycles. For 2-dimensional representations, Theta cycles are (the Selmer images of) Heegner points. In general, they conjecturally exhibit an analogous strong relation with the Beilinson–Bloch–Kato conjectures in rank 1, for which we gather the available evidence.

Original languageAmerican English
JournalJournal of Number Theory
StateAccepted/In press - 1 Jan 2024


  • Beilinson–Bloch–Kato conjectures
  • Galois representations
  • Kudla program
  • Unitary Shimura varieties

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


Dive into the research topics of 'Theta cycles and the Beilinson–Bloch–Kato conjectures'. Together they form a unique fingerprint.

Cite this