Seminar

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Let F be a p-adic local field. The linear Arithmetic Fundamental Lemma Conjecture, due to Qirui Li, relates the derivatives of certain orbital integrals on GL_{2n}(F) with certain intersection numbers on moduli spaces of p-divisible groups. More precisely, the orbital integrals in question are taken for spherical Hecke functions and the intersection numbers for Lubin--Tate moduli spaces.

In joint work with Qirui Li, we formulate a similar conjecture, but for orbital integrals of parahoric type Hecke functions and intersection numbers on EL-type moduli spaces for central simplealgebras. In my talk, I will explain this conjecture and its proof for division algebras of invariant 1/4 and 3/4.