I am in the process of ordering some book on the Langlands program, and learning more about it. In the mean time, I have a question which is easy to the experts, but being a beginner, I am not a 100% sure, so I could use some confirmation (or the opposite!).
In a trace formula, the geometric side is the trace of the matrix, which is the sum of the diagonal entries, while the spectral side is the sum of the eigenvalues. That these 2 sums are equal is the content of the trace formula.
If one were to label one side of the Langlands program as geometric, and the other as spectral, which side would that be?
If I were to guess, I would say that perhaps the Galois side is the spectral side, while the automorphic side is the geometric side, because I think that the Galois side is the side containing the information that we would like to obtain, so it is the spectral side, while the automorphic side is supposedly easier to calculate. Am I right, or do I have the analogy backwards?
Edit: A paper by Gaitsgory confirms my suspicion: http://www.math.harvard.edu/~gaitsgde/GL/outline.pdf in 0.2.1. The "Galois" side is the "spectral" side, while the "automorphic" side is the "geometric" side, according to Gaitsgory.
I have decided to answer my own question, since I found a paper by Gaitsgory which confirms my suspicion:
http://www.math.harvard.edu/~gaitsgde/GL/outline.pdf in 0.2.1. The "Galois" side is the "spectral" side, while the "automorphic" side is the "geometric" side, according to Gaitsgory.
I am still very shaky about the Langlands program, which is why I am planning to order an introductory book. Actually, I only found one introductory book, called "An introduction to the Langlands Program", with various authors contributing to the book. If someone happens to know of some other introductory textbooks, could you please post it as a comment perhaps?