Cohomologie relative des formes cuspidales

TL;DR

This paper proves that modular cusp forms do not have higher direct images between toroidal and minimal compactifications, clarifying their cohomological behavior in algebraic geometry.

Contribution

It establishes a new result on the vanishing of higher direct images for cusp forms between specific compactifications, advancing understanding in the cohomology of modular forms.

Findings

Higher direct images vanish for cusp forms between compactifications

Results apply to the cohomological analysis of modular forms

Clarifies the relationship between different compactifications in algebraic geometry

Abstract

In this note, we show that modular cusp forms have no higher direct images between toroidal and minimal compactifiations. --- Dans cette note, nous montrons que les faisceaux de formes modulaires cuspidales n'ont pas d'image directe superieure entre compactifications toroidale et minimale.