Rigid cohomology
In mathematics, rigid cohomology is a p-adic cohomology theory introduced by . It extends crystalline cohomology to schemes that need not be proper or smooth, and extends Monsky–Washnitzer cohomology
Modularity theorem
The modularity theorem (formerly called the Taniyama–Shimura conjecture, Taniyama-Weil conjecture or modularity conjecture for elliptic curves) states that elliptic curves over the field of rational n
Néron–Ogg–Shafarevich criterion
In mathematics, the Néron–Ogg–Shafarevich criterion states that if A is an elliptic curve or abelian variety over a local field K and ℓ is a prime not dividing the characteristic of the residue field
Complex multiplication of abelian varieties
In mathematics, an abelian variety A defined over a field K is said to have CM-type if it has a large enough commutative subring in its endomorphism ring End(A). The terminology here is from complex m
Section conjecture
In anabelian geometry, a branch of algebraic geometry, the section conjecture gives a conjectural description of the splittings of the group homomorphism , where is a complete smooth curve of genus at
P-adic Hodge theory
In mathematics, p-adic Hodge theory is a theory that provides a way to classify and study p-adic Galois representations of characteristic 0 local fields with residual characteristic p (such as Qp). Th
Arithmetic variety
In mathematics, an arithmetic variety is the quotient space of a Hermitian symmetric space by an arithmetic subgroup of the associated algebraic Lie group.
Arithmetic geometry
In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the stud
Uniform boundedness conjecture for rational points
In arithmetic geometry, the uniform boundedness conjecture for rational points asserts that for a given number field and a positive integer that there exists a number depending only on and such that f
Anabelian geometry
Anabelian geometry is a theory in number theory which describes the way in which the algebraic fundamental group G of a certain arithmetic variety X, or some related geometric object, can help to rest