Category

Topological methods of algebraic geometry

page 1

collection of objects associated to subsets of a space in a manner admitting gluing and restriction

Riemann–Roch theorem

theorem that the Euler characteristic of the sheaf cohomology of a holomorphic line bundle on a Riemann surface equals the degree of the bundle plus half of the Euler characteristic of the surface

Weil conjectures

sheaf cohomology

right derived functors of the global sections functor Γ: AbSh → Ab

abelian group related to division algebras

conjectural objects in algebraic geometry that provide a universal cohomology theory of varieties

Hirzebruch–Riemann–Roch theorem

on the Euler characteristic of a holomorphic vector bundle on a compact complex manifold

etale cohomology

sheaf cohomology on the étale site

Grothendieck–Hirzebruch–Riemann–Roch theorem

Result in algebraic geometry

finite-type sheaf F of modules over a ringed space such that the kernel of a surjective morphism from a finite direct sum of the structure sheaf onto it is also of finite type

Analogs of homology groups for algebraic varieties

Lefschetz hyperplane theorem

theorem that the inclusion between a projective variety and its hyperplane section induces isomorphisms of homology, cohomology or homotopy groups in low degrees

étale fundamental group

topological concept in algebraic geometry

Riemann–Roch theorem for surfaces

Mathematical theorem

motivic cohomology

invariant of algebraic varieties and of more general schemes

duality for holomorphic vector bundles on a compact complex manifold induced by a dualizing sheaf

Tate conjecture

conjecture in algebraic geometry