# Conjectures

### Some articles on conjectures, conjecture:

Michael J. Hopkins - Work - The Ravenel Conjectures
... For more details on this topic, see Ravenel conjectures ... The Ravenel conjectures very roughly say complex cobordism (and its variants) see more in the stable homotopy category than you might think ... For example, the nilpotence conjecture states that some suspension of some iteration of a map between finite CW-complexes is null-homotopic iff it is zero in complex cobordism ...
Timeline Of Number Theory - 18th Century
... 1742 - Christian Goldbach conjectures that every even number greater than two can be expressed as the sum of two primes, now known as Goldbach's conjecture ... In the same year, Edward Waring conjectures Waring's problem, that for any positive integer k, every positive integer is the sum of a fixed number of kth powers. 1796 - Adrien-Marie Legendre conjectures the prime number theorem ...
Alexander Beilinson - Work
... In 1981 Beilinson announced a proof of the Kazhdan–Lusztig conjectures and Jantzen conjectures with Joseph Bernstein ... and Bernstein, Brylinski and Kashiwara obtained a proof of the Kazhdan–Lusztig conjectures ... In 1982 Beilinson stated his own, seemingly profound conjectures about the existence of motivic cohomology groups for schemes, provided as hypercohomology ...
Cristian Dumitru Popescu
... and proved function-field versions of the Gras conjectures and Rubin's integral refinement of the abelian Stark conjectures ... He has also made important contributions to the Stark conjectures over number fields, formulating an alternative to Rubin's refinement, known as Popescu's ... Although slightly weaker than Rubin's conjecture, it has the advantage that it can presently be shown to remain true under raising the base field or lowering the top field of the extension ...
Arthur Conjectures
... In mathematics, the Arthur conjectures are some conjectures about automorphic representations of reductive groups over the adeles and unitary representations of reductive groups over local ... Arthur's conjectures imply the generalized Ramanujan conjectures for cusp forms on general linear groups ...

### Famous quotes containing the word conjectures:

Our conjectures pass upon us for truths; we will know what we do not know, and often, what we cannot know: so mortifying to our pride is the base suspicion of ignorance.
Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)

After all, it is putting a very high price on one’s conjectures to have a man roasted alive because of them.
Michel de Montaigne (1533–1592)