An arithmetic intersection conjecture
Brian Smithling
TL;DR
This paper surveys recent joint work on the arithmetic Gan-Gross-Prasad conjecture, focusing on Shimura varieties associated with unitary groups, and discusses new insights into their intersection theory.
Contribution
It presents a comprehensive overview of recent advances in the arithmetic intersection conjecture for unitary Shimura varieties, highlighting novel techniques and results.
Findings
Progress towards the arithmetic Gan-Gross-Prasad conjecture
New results on intersection numbers of special cycles
Connections between automorphic forms and arithmetic geometry
Abstract
We survey recent joint work with M. Rapoport and W. Zhang related to the arithmetic Gan-Gross-Prasad conjecture for Shimura varieties attached to unitary groups.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Advanced Combinatorial Mathematics