- abc conjecture
- The abc conjecture of Masser and Oesterlé attempts to state as much as possible about repeated prime factors in an equation a + b = c. For example 3 + 125 = 128 but the prime powers here are exceptional.
- Arakelov class group
- The Arakelov class group is the analogue of the ideal class group or divisor class group for Arakelov divisors.
- Arakelov divisor
- An Arakelov divisor (or replete divisor) on a global field is an extension of the concept of divisor or fractional ideal. It is a formal linear combination of places of the field with finite places having integer coefficients and the infinite places having real coefficients.
- Arakelov height
- The Arakelov height on a projective space over the field of algebraic numbers is a global height function with local contributions coming from Fubini–Study metrics on the Archimedean fields and the usual metric on the non-Archimedean fields.
- Arakelov theory
- Arakelov theory is an approach to arithmetic geometry that explicitly includes the 'infinite primes'.
- Arithmetic of abelian varieties
- See main article arithmetic of abelian varieties
- Artin L-functions
- Artin L-functions are defined for quite general Galois representations. The introduction of étale cohomology in the 1960s meant that Hasse–Weil L-functions could be regarded as Artin L-functions for the Galois representations on l-adic cohomology groups.
Read more about this topic: Glossary Of Arithmetic And Diophantine Geometry