functoriality造句

• This functoriality conjecture implies all the other conjectures presented so far.
• Functoriality of the total Chern classes allows one to write this relation as
• He then goes on to formulate a very general " Functoriality Principle ".
• The second property expresses the " functoriality " of a ?-functor.
• For reductive groups other than, the generalized Ramanujan conjecture would follow from principle of Langlands functoriality.
• Functoriality is the conjecture that automorphic forms on different groups should be related in terms of their-groups.
• A proof of Langlands functoriality would also lead towards a thorough understanding of the analytic properties of automorphic L-functions.
• Roughly speaking, the Langlands reciprocity conjecture is the special case of the functoriality conjecture when one of the reductive groups is trivial.
• It is an observation due to functoriality of symmetric powers of automorphic representations of will give a proof of the Ramanujan Petersson conjecture.
• His joint work with Robert Langlands and Ng?B?o Ch鈛 suggested a new approach to the functoriality of automorphic representations and trace formulas.
• The generalized Ramanujan conjecture in turn follows from the Langlands functoriality conjecture, and this has led to some progress on Selberg's conjecture.
• It was in this letter that he introduced what has since become known as the-group and along with it, the notion of functoriality.
• A great deal is known about the cohomology of groups, including interpretations of low-dimensional cohomology, functoriality, and how to change groups.
• In its application to Artin's conjecture, functoriality associated to every-dimensional representation of a Galois group an automorphic representation of the adelic group of.
• In general, the Langlands functoriality conjectures imply that automorphic L-functions of a connected reductive group are equal to products of automorphic L-functions of general linear groups.
• This includes proving fundamental properties, such as the contravariant functoriality and a projective bundle formula, as well as constructing an action of the usual higher Chow groups on the additive ones ."
• The functoriality conjecture states that a suitable homomorphism of L-groups is expected to give a correspondence between automorphic forms ( in the global case ) or representations ( in the local case ).
• In this formulation, the multiplicativity property C _ k ( AB ) = C _ k ( A ) C _ k ( B ) is equivalent to the functoriality of the exterior power.
• Functoriality, the-group, the rigorous introduction of adele groups, and the consequent application of the representation theory of reductive groups over local fields changed drastically the way research in automorphic forms was carried out.
• What initially was very new in Langlands'work, besides technical depth, was the proposed direct connection to number theory, together with the rich organisational structure hypothesised ( so-called " functoriality " ).