mathematics, the standard conjectures about algebraic cycles are several conjectures describing the relationship of algebraic cycles and Weil cohomology...

Grothendieck's standard conjectures on algebraic cycles yield enough cycles to construct his category of motives and would imply that algebraic cycles play a...

number theory and algebraic geometry, the Tate conjecture is a 1963 conjecture of John Tate that would describe the algebraic cycles on a variety in terms...

analogue of the Weil conjectures for Kähler manifolds, Grothendieck envisioned a proof based on his standard conjectures on algebraic cycles (Kleiman 1968)...

of algebraic curves Motive (algebraic geometry) Perverse sheaf Riemann–Hilbert correspondence Serre's modularity conjecture Standard conjectures on algebraic...

{\displaystyle k} . Standard conjectures on algebraic cycles Tate conjecture on the connection between algebraic cycles on algebraic varieties and Galois...

This is a list of notable mathematical conjectures. The following conjectures remain open. The (incomplete) column "cites" lists the number of results...

the triangulated category. The standard conjectures were first formulated in terms of the interplay of algebraic cycles and Weil cohomology theories. The...

(mathematics) Section conjecture Semistable abelian variety Sheaf cohomology Stack (mathematics) Standard conjectures on algebraic cycles Sketch of a program...

this version became standard. In 1996, László Babai published a conjecture sharply contradicting this conjecture, but both conjectures remain widely open...

In algebraic geometry, a branch of mathematics, an adequate equivalence relation is an equivalence relation on algebraic cycles of smooth projective varieties...

exception consists of three conjectures made by André Weil in the late 1940s (the Weil conjectures). In the fields of algebraic geometry, number theory and...

closely related to certain standard conjectures on algebraic cycles and vanishing conjectures, such as the Beilinson-Soulé conjecture. In the above example...

connections to Alexander Grothendieck's standard conjectures on algebraic cycles. Macintyre has proved many results on the model theory of real and complex...

complex algebraic varieties. Arithmetic dynamics is the study of the number-theoretic properties of integer, rational, p-adic, or algebraic points under...

of algebraic varieties and of more general schemes. It is a type of cohomology related to motives and includes the Chow ring of algebraic cycles as a...

has become an important tool in algebraic geometry, particularly through its connection to the study of algebraic cycles. While Hodge theory is intrinsically...

(not only algebraic ones). At its origin, it was introduced, together with homological algebra for allowing the algebraic study of non-algebraic objects...

to any other adequate equivalence relation on algebraic cycles. Some of the deepest conjectures in algebraic geometry and number theory are attempts to...

encompass large parts of number theory and algebraic geometry. Much of the theory is in the form of proposed conjectures, which can be related at various levels...

have a diagram that is simultaneously alternating and algebraic. It follows from the Tait conjectures that the crossing number of the Borromean rings (the...

linear algebraic groups over the field of real or complex numbers. (For example, every compact Lie group can be regarded as a linear algebraic group over...

Categories of abstract algebraic structures including representation theory and universal algebra; Homological algebra; Homotopical algebra; Topology using categories...

are called algebraic integers. A period is a complex number that can be expressed as an integral of an algebraic function over an algebraic domain. The...

reworking of the foundations of algebraic geometry. It has become the most important foundational work in modern algebraic geometry. The approach expounded...

glossary of properties and concepts in algebraic topology in mathematics. See also: glossary of topology, list of algebraic topology topics, glossary of category...

Deninger proved that classical conjectures of Beilinson and Bloch concerning the intersection theory of algebraic cycles would be further consequences...

an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry. The prime ideals of the ring of integers are...

Unsolved problem in mathematics Conjecture: Every bridgeless graph has a cycle-continuous mapping to the Petersen graph. More unsolved problems in mathematics...

clique number of G {\displaystyle G} . The Hadwiger conjecture can be stated in the simple algebraic form χ ( G ) ≤ h ( G ) {\displaystyle \chi (G)\leq...