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### Is there a Grothendieck-Riemann-Roch type of theorem generalizing Grothendieck's Lefschetz trace formula

Grothendieck deduced that the L-function of a (constructible) $\ell$-adic sheaf on a variety over $\mathbf{F}_p$ is rational from the generalized trace formula.
My first question is based on the ...

**14**

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### Computation of low weight Siegel modular forms

We have these huge tables of elliptic curves, which were generated by computing modular forms of weight 2 and level Gamma_0(N) as N increased.
For abelian surfaces over $\mathbf{Q}$ we have very ...

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### What is the Twisted Trace Formula?

I am studying the trace formula using "An Introduction to the Trace Formula" by James Arthur. I would like to understand the twisted trace formula, but unfortunately I never came across a good ...

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### On Langlands Pairing and transfer factors

In the paper "On the definition of transfer factors" Langlands and Shelstad define a certain number of factors $\Delta_{I}$, $\Delta_{II}$,$\Delta_{III,1}$,$\Delta_{III,2}$, which are roots of unity.
...

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### base change and Langlands' combinatorial exercise

Hi,
Is it correct that Langlands' combinatorial exercise (as he terms it in his paper
"Shimura varieties and the Selberg trace formula") is to establish base change identities between orbital ...

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232 views

### on the fundamental lemma

I consider the fundamental lemma for the spherical Hecke algebra.
Let $G$ a connected reductive quasisplit group on $F$, a local field of equal characteristic $p$.
and $H$ an endoscopic group.
Can ...

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23 views

### linearization method in smooth transfer of relative trace formula

I'm currently reading Jacquet's paper 'smooth transfer of Kloosterman integrals', in which Jacquet proved there is a smooth transfer for compactly supported smooth functions on GL(n,F) to smooth ...

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52 views

### stablization of cuspidal terms

Kottwitz, building on the work of Langlands and Shelstad, gave a stabilization of the elliptic terms on the geometric side of the trace formula. This stabilization depended on the endoscopic transfer ...