Diagonal cycles on Shtukas and the adjoint L-function

2026/07/28 by Zeyu Wang
Mathematics · #math.NT #math.AG #math.RT

paper · pdf

Abstract

We study diagonal cycles on moduli spaces of shtukas for groups of the form H× H, where H is a split almost simple reductive group, allowing arbitrary modification types. We relate their self-intersection numbers, with insertions of determinant line bundles, to higher derivatives of adjoint L-functions. This gives a general Gross--Zagier-type identity over function fields for groups of arbitrary type, and suggests a parallel conjectural picture for arithmetic intersections on Shimura varieties.

Citations

• Special Cycle on Shtukas and Categorical Trace
• Geometric Langlands in positive characteristic from characteristic zero
• Higher Period Integrals and Derivatives of L-functions
• A "strange" functional equation for Eisenstein series and miraculous duality on the moduli stack of bundles
• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups

Related

• Intersection formulas on moduli spaces of unitary shtukas
• Shtukas and the Taylor expansion of L-functions
• Special Cycle on Shtukas and Categorical Trace
• Manin-Drinfeld cycles and derivatives of L-functions
• Special cycles on unitary Shimura varieties II: global theory