分野別セミナー

This is a survey talk on joint papers with A.N. Parshin about how to
construct the main ingredients of harmonic analysis for adelic rings of
two-dimensional arithmetic schemes (the main difficulty is that this
adelic ring is not locally compact). The application of the theory is a
new proof of the Riemann-Roch theorem for algebraic surfaces over finite
fields, using the analogs of Poisson formulas like the well-known proof
for algebraic curves by means of usual harmonic analysis. The references
are arXiv:0707.1766v3 [math.AG], arXiv:0912.1577v2 [math.AG] and
arXiv:1107.0408v2 [math.AG].