In mathematics, the Weil conjecture on Tamagawa numbers is the statement that the Tamagawa number τ ( G ) {\displaystyle \tau (G)} of a simply connected...

Lurie, Jacob (2014), Tamagawa Numbers via Nonabelian Poincaré Duality Gaitsgory, Dennis; Lurie, Jacob (2019), Weil's Conjecture for Function Fields (Volume...

Taniyama–Shimura–Weil conjecture about elliptic curves, proved by Wiles and others. The Weil conjecture on Tamagawa numbers about the Tamagawa number of an...

possible assuming Weil's conjecture on Tamagawa numbers. The conjecture asserts for the case of the algebraic group SL2(R) that the Tamagawa number of the...

anticipation of later ideas such as moduli spaces of bundles. The Weil conjecture on Tamagawa numbers proved resistant for many years. Eventually the adelic approach...

conjecture Kelvin's conjecture Kouchnirenko's conjecture Mertens conjecture Pólya conjecture, 1919 (1958) Ragsdale conjecture Schoenflies conjecture (disproved...

deep way to the distribution of prime numbers. This is a special case of Weil's conjecture on Tamagawa numbers, which asserts the equality of similar...

Tamagawa number of E at a prime p dividing the conductor N of E. It can be found by Tate's algorithm. At the time of the inception of the conjecture little...

Tamagawa numbers The direct Tamagawa number definition works well only for linear algebraic groups. There the Weil conjecture on Tamagawa numbers was...

University Press. ISBN 0198503415. Gaitsgory, Dennis; Lurie, Jacob (2019). Weil's Conjecture for Function Fields (Volume I). Annals of Mathematics Studies. Vol...

Map Weil–Châtelet group Weil cohomology Weil conjecture (disambiguation) Weil conjectures Weil conjecture on Tamagawa numbers Weil's criterion Weil–Deligne...

form (Lie theory), Satake diagram Adelic algebraic group, Weil's conjecture on Tamagawa numbers Langlands classification, Langlands program, geometric Langlands...

algebra, Deligne–Lusztig theory Real form (Lie theory) Weil's conjecture on Tamagawa numbers Langlands classification, Langlands dual group, Langlands...

principle for algebraic groups was used in the proofs of the Weil conjecture for Tamagawa numbers and the strong approximation theorem. Local analysis Grunwald–Wang...

series induced from cusp forms on smaller subgroups. As a first application, he proved the Weil conjecture on Tamagawa numbers for the large class of arbitrary...

prove the Weil conjecture on Tamagawa numbers. Lafforgue (2002) described how the trace formula is used in his proof of the Langlands conjecture for general...

http://www.uni-essen.de/~hm0002/. Gaitsgory, Dennis; Lurie, Jacob (2019), Weil's conjecture for function fields, Vol. 1 (PDF), Annals of Mathematics Studies,...

equivariant Tamagawa number conjecture: a survey", in Burns, David; Popescu, Christian; Sands, Jonathan; et al. (eds.), Stark's conjectures: recent work...

André Weil found evidence supporting it, yet no proof; as a result the "astounding" conjecture was often known as the Taniyama–Shimura-Weil conjecture. It...

saying that the Tamagawa number of its simply connected cover the spin group is 1. André Weil conjectured more generally that the Tamagawa number of any...

algebraic K-theory and Tamagawa measures, modern number theory deals with a description, if largely conjectural (see Tamagawa number conjecture), of values of...