The fundamental lemma of Jacquet-Rallis in positive characteristics

Transfer to characteristic zero: appendix to "Fundamental Lemma of Jacquet-Rallis in positive characteristics" by Zhiwei Yun

This appendix shows that the Fundamental lemma of Jacquet-Rallis, proved by Zhiwei Yun in the positive charactersitic case, is also true in characteristic zero, when residue characteristic is sufficiently large. In fact, this follows immediately from the article "Transfer Principle for the Fundamental Lemma" by R. Cluckers, T.C. Hales and F.Loeser.

球面海加以尔代数的相对基本引理与乘法希钦纤维化：雅各布森-拉里斯情况

Relative Fundamental Lemmas for Spherical Hecke Algebras and Multiplicative Hitchin Fibrations: the Jacquet--Rallis Case

本文通过乘法希钦纤维化方法，证明了局部函数域上球面海加以尔代数的雅各布森-拉里斯基本引理。

Transfer factors for Jacquet-Mao's metaplectic fundamental lemma

In an earlier paper we proved Jacquet-Mao's metaplectic fundamental lemma which is the identity between two orbital integrals (one is defined on the space of symmetric matrices and another one is defined on the $2$-fold cover of the general linear group) corrected by a transfer factor. But we restricted to the case where the relevant representative is a diagonal matrix. Now, we show that we can extend this result for the more general relevant representative. Our proof is based on the concept of Shalika germs for certain Kloosterman integrals.

Le lemme fondamental métaplectique de Jacquet et Mao en égales caractéristiques

We prove in the case of equal characteristic a fundamental lemma conjectured by Jacquet and Mao for the metaplectic group. We use the arguments of Bao Châu Ngô for Jacquet-Ye's fundamental lemma and a geometric study of the metaplectic extension.

Faisceaux pervers, homomorphisme de changement de base et lemme fondamental de Jacquet et Ye

We give a geometric interpretation of the base change homomorphism between the Hecke algebra of GL(n) for an unramified extension of local fields of positive characteristic. For this, we use some results of Ginzburg, Mirkovic and Vilonen related to the geometric Satake isomorphism. We give new proof for these results in the positive characteristic case. By using that geometric interpretation of the base change homomorphism, we prove the fundamental lemma of Jacquet and Ye for arbitrary Hecke function in the the equal characteristic case.

$GL_{2n}$ 内形式的算术转移

Arithmetic transfer for inner forms of $GL_{2n}$

本文为 $GL_{2n}$ 的内形式提出了 Guo--Jacquet 型基本引理猜想和算术转移猜想，并证明了这些猜想对于不变量为 $1/4$ 和 $3/4$ 的除法代数成立。