Further reading

This edition contains the nine lessons and their linked supporting readings.

Higher-dimensional cycle classes and trace formulas

Smooth traces, duality and Gysin maps proves the relative curve trace, coordinate independence, higher-dimensional smooth trace and its duality consequences. The cycle-class lesson uses these proved constructions.

The Riemann hypothesis for curves

Section 2 of the cycle-class lesson proves the surface Hodge index theorem, including its equality clause. Section 5 applies it to Frobenius graphs and proves the Riemann hypothesis for curves.

Earlier companion chapters that omitted these arguments are still excluded from this edition. The linked proofs above supply the prerequisites used here.

Browse available prerequisites

Higher-dimensional pencils

The Lefschetz-pencil lesson proves the local quadratic calculation and variation, tame generation, geometric conjugacy, the exceptional sheaf alternative and symplectic openness. It links the exact completed prerequisite readings.

Smooth proper purity and rationality

The full rationality and Riemann-hypothesis lessons are being revised with their precise smooth-projective alteration prerequisite. The available determinant, conductor and Tate-curve proofs supply the corresponding prerequisites for the fundamental estimate.