<div>Geometric Reformulation of the Riemann Hypothesis via Sheaf Theory</div>

This paper proposes a geometric reformulation of the Riemann Hypothesis using tools from modern sheaf theory and algebraic geometry. By encoding the zero distribution of the Riemann zeta function into the cohomological behavior of sheaves over arithmetic schemes, we construct a sheaf-theoretic model of the critical line. The key insight involves interpreting zeros as fixed points under functorial gluing conditions and associating them with the vanishing loci of derived sheaf cohomology groups. We further analyze the stalk regularity and arithmetic torsion of sheaves over , drawing parallels with spectral sequences and étale topologies. This framework provides a new perspective on the Riemann Hypothesis as a condition of geometric regularity and cohomological alignment, potentially paving the way for a categorical and topological resolution.