Near center derivatives and arithmetic 1-cycles

Degrees of arithmetic special cycles on Shimura varieties are expected to appear in first derivatives of automorphic forms and L-functions, such as in the Gross–Zagier formula, Kudla’s program, and the Arithmetic Gan–Gross–Prasad program.

I will explain some “near-central” instances of an arithmetic Siegel–Weil formula from Kudla’s program, which “geometrize” the classical Siegel mass and Siegel–Weil formulas, on lattice and lattice vector counting.

At these near-central points of functional symmetry, it is typical that both the “leading” special value (complex volumes) and the “subleading” first derivative (arithmetic volume) simultaneously have geometric meaning.

The key input is a new “limit phenomenon” relating positive characteristic intersection numbers and heights in mixed characteristic, as well as its automorphic counterpart.

A pretalk will be giving at 2:00 in room 530.

Pretalk: I’ll give an introduction to some basic arithmetic intersection theory.