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Cohen [4] [7] showed that CH cannot be proven from the ZFC axioms, completing the overall independence proof. To prove his result, Cohen developed the method of forcing, which has become a standard tool in set theory. Essentially, this method begins with a model of ZF in which CH holds, and constructs another model which contains more sets than ...
In algebraic topology, the doomsday conjecture was a conjecture about Ext groups over the Steenrod algebra made by Joel Cohen, named by Michael Barratt, published by Milgram (1971, conjecture 73) and disproved by Mahowald (1977). Minami (1995) stated a modified version called the new doomsday conjecture.
Then there exists an R-algebra B R that is a balanced big Cohen–Macaulay algebra for R, an S-algebra that is a balanced big Cohen-Macaulay algebra for S, and a homomorphism B R → B S such that the natural square given by these maps commutes. Serre's Conjecture on Multiplicities. (cf. Serre's multiplicity conjectures.
This is one of the central problems of number theory, incorporating earlier conjectures by Deligne and Beilinson. The Birch–Swinnerton-Dyer conjecture is a special case. More precisely, the conjecture predicts the leading coefficient of the L-function at an integer point in terms of regulators and a height pairing on motivic cohomology.
In philosophy, Occam's razor (also spelled Ockham's razor or Ocham's razor; Latin: novacula Occami) is the problem-solving principle that recommends searching for explanations constructed with the smallest possible set of elements.
The Hodge standard conjecture is not to be confused with the Hodge conjecture which states that for smooth projective varieties over C, every rational (p, p)-class is algebraic. The Hodge conjecture implies the Lefschetz and Künneth conjectures and conjecture D for varieties over fields of characteristic zero.
In topology, Brown–Gitler spectrum is related to the concepts of the Segal conjecture (proven in 1984) and the Burnside ring. [4] Applications.
Richard Ewen Borcherds (/ ˈ b ɔːr tʃ ər d z /; born 29 November 1959) [2] is a British [4] mathematician currently working in quantum field theory.He is known for his work in lattices, group theory, and infinite-dimensional algebras, [5] [6] for which he was awarded the Fields Medal in 1998.