nLab arithmetic geometry - contents

number theory

• arithmetic

• arithmetic geometry, arithmetic topology

• higher arithmetic geometry, E-∞ arithmetic geometry

number

• natural number, integer number, rational number, real number, irrational number, complex number, quaternion, octonion, adic number, cardinal number, ordinal number, surreal number

arithmetic

• Peano arithmetic, second-order arithmetic

• transfinite arithmetic, cardinal arithmetic, ordinal arithmetic

• prime field, p-adic integer, p-adic rational number, p-adic complex number

arithmetic geometry, function field analogy

• arithmetic scheme

  • arithmetic curve, elliptic curve

  • arithmetic genus

• arithmetic Chern-Simons theory

• arithmetic Chow group

• Weil-étale topology for arithmetic schemes

• absolute cohomology

• Weil conjecture on Tamagawa numbers

• Borger's absolute geometry

• Iwasawa-Tate theory

  • arithmetic jet space

• adelic integration

• shtuka

• Frobenioid

Arakelov geometry

• arithmetic Riemann-Roch theorem

• differential algebraic K-theory