WebApr 11, 2024 · The Mumford-Tate conjecture asserts that, via the Betti-étale comparison isomorphism, and for any smooth projective variety X, over a number field K, the Q ℓ -linear combinations of Hodge cycles coincide with the ℓ -adic Tate cycles. Question. WebTate[1965, Conjecture 2]further made a conjecture relating algebraic cycles to poles of zeta functions (often known as the strong Tate conjecture). When F is a number field, we denote byL(H2r(X)(r),s)the (incomplete) L-function associated to the compatible system {H2r(X F,Qℓ(r))}of 0 F-representations, which
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In 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 of a more computable invariant, the Galois representation on étale cohomology. The conjecture is a central problem in the theory of algebraic cycles. It can be … See more Let V be a smooth projective variety over a field k which is finitely generated over its prime field. Let ks be a separable closure of k, and let G be the absolute Galois group Gal(ks/k) of k. Fix a prime number ℓ which is invertible in k. … See more The Tate conjecture for divisors (algebraic cycles of codimension 1) is a major open problem. For example, let f : X → C be a morphism from a … See more • James Milne, The Tate conjecture over finite fields (AIM talk). See more Let X be a smooth projective variety over a finitely generated field k. The semisimplicity conjecture predicts that the representation of … See more WebJul 25, 2024 · On the Tate Conjecture in Codimension One for Varieties with over Finite Fields Paul Hamacher, Ziquan Yang, Xiaolei Zhao We prove that the Tate conjecture over finite fields is ''generically true'' for mod reductions of complex projective varieties with , under a mild assumption on moduli. joy nash fantastic fiction
Andrew Tate, Nietzsche and the Matrix Alexis Papazoglou
WebThe Tate conjecture over finite fields (AIM talk) J.S. Milne Abstract These are my notes for a talk at the The Tate Conjecture workshop at the American Institute of Mathematics in Palo Alto, CA, July 23–July 27, 2007, somewhat revised and expanded. The intent of the talk was to review what is known and to suggest directions for research. WebThe Tate Conjecture for Certain Abelian Varieties over Finite Fields. EN. English Deutsch Français Español Português Italiano Român Nederlands Latina Dansk Svenska Norsk Magyar Bahasa Indonesia Türkçe Suomi Latvian Lithuanian česk ... WebTate’s conjecture holds and rational and numerical equivalence over finite fields agree, then higher rational K-groups of smooth projective varieties over finite fields vanish … joy mz los wh nat