Schemes

• Scheme implementation overview
• Schemes
• The Spec functor
• Scheme obtained by gluing two other schemes
• Points on schemes
• Ambient spaces
• Algebraic schemes
• Hypersurfaces in affine and projective space
• Set of homomorphisms between two schemes
• Scheme morphism
• Divisors on schemes
• Divisor groups

Affine Schemes

• Affine \(n\) space over a ring
• Morphisms on affine schemes
• Points on affine varieties
• Subschemes of affine space
• Enumeration of rational points on affine schemes
• Set of homomorphisms between two affine schemes

Projective Schemes

• Projective \(n\) space over a ring
• Morphisms on projective schemes
• Points on projective varieties
• Subschemes of projective space
• Enumeration of rational points on projective schemes
• Set of homomorphisms between two projective schemes

Products of Projective Spaces

• Products of projective spaces
• Set of homomorphisms
• Polynomial morphisms for products of projective spaces
• Points for products of projective spaces
• Subschemes of products of projective spaces
• Enumeration of rational points on product projective schemes

Toric Varieties

• Toric varieties
• Fano toric varieties
• Library of toric varieties
• Toric divisors and divisor classes
• Toric rational divisor classes
• The Chow group of a toric variety
• Toric ideals
• Morphisms of toric varieties
• Subschemes of toric space
• Weierstrass form of a toric elliptic curve
• Map to the Weierstrass form of a toric elliptic curve
• Weierstrass for elliptic curves in higher codimension
• Set of homomorphisms between two toric varieties
• Enumerate points of a toric variety
• Construct sheaves on toric varieties
• Klyachko bundles and sheaves

Cyclic Covers

• Cyclic covers over a finite field
• Cyclic covers curves over a general ring
• Computation of the Frobenius polynomial using Newton’s identities
• Cyclic cover curve constructor

Berkovich Analytic Space

• Elements of Berkovich space.
• Berkovich Space over \(\CC_p\)

Indices and Tables

• Index

• Module Index

• Search Page