The contrasting case of real quadratic fields is very different, and much less is known. That is because what enters the analytic formula for the class number is not h, the class number, on its own — ...
History of algebraic number theory Diophantus The beginnings of algebraic number theory can be traced to Diophantine equations, named for the 3rd-century Alexandrian mathematician, Diophantus, who stu ...
Suppose that Mg,n is the moduli stack of compact Riemann surfaces of genus g with n distinct marked points x1,...,xn, and Mg,n is its Deligne–Mumford compactification. There are n line bundles Li on ...
In algebraic geometry, the Virasoro conjecture states that a certain generating function encoding Gromov–Witten invariants of a smooth projective variety is fixed by an action of half of the Virasoro ...
In anabelian geometry, the section conjecture gives a conjectural description of the splittings of π1(X) → Gal(k), where X is a complete smooth curve of genus at least 2 over a field k that is finit ...
In mathematics, the standard conjectures about algebraic cycles are several conjectures describing the relationship of algebraic cycles and Weil cohomology theories. One of the original applications o ...
Originally the problem of resolution of singularities was to find a nonsingular model for the function field of a variety X, in other words a complete non-singular variety X′ with the same function f ...
In mathematics, the Nakai conjecture is an unproven characterization of smooth algebraic varieties, conjectured by Japanese mathematician Yoshikazu Nakai in 1961. It states that if V is a complex alge ...
In mathematics, the Manin conjecture was proposed by Yuri I. Manin and his collaborators in 1989 when they initiated a program with the aim of describing the distribution of rational points on suitabl ...
The Jacobian Determinant Let N 1 be a fixed integer and consider the polynomials f1, ..., fN in variables X1, ..., XN with coefficients in an algebraically closed field k (in fact, it suffices to ass ...
In mathematics, Fujita's conjecture is a problem in the theories of algebraic geometry and complex manifolds, unsolved as of 2013.In complex manifold theory, the conjecture states that for a positive ...
In algebraic geometry, the Fr?berg conjecture, introduced by Fr?berg (1985,?page 120), is a conjecture about the possible Hilbert functions of a set of forms. The Fr?berg–Iarrobino conjecture is ...
In mathematics, there are a number of so-called Deligne conjectures, provided by Pierre Deligne. These are independent conjectures in various fields of mathematics.The Deligne conjecture in deformatio ...
Any of the following equivalent statements is referred to as the Bass conjecture.For any finitely generated Z-algebra A, the groups K'n(A) are finitely generated (K-theory of finitely generated A-modu ...
The conjecture in its modern form is as follows. Let S be a Shimura variety and let V be a set of special points in S. Then the irreducible components of the Zariski closure of V are special subvariet ...
