Grothendieck conjecture
In positive characteristic the Hodge standard conjecture is known for surfaces (Grothendieck (1958)) and for abelian varieties of dimension 4 (Ancona (2024)). The Hodge standard conjecture is not to be confused with the Hodge conjecture which states that for smooth projective varieties over C , every … See more In mathematics, the standard conjectures about algebraic cycles are several conjectures describing the relationship of algebraic cycles and Weil cohomology theories. One of the original applications of these conjectures, … See more Conjecture D states that numerical and homological equivalence agree. (It implies in particular the latter does not depend on the choice of the Weil cohomology theory). This conjecture implies the Lefschetz conjecture. If the Hodge standard conjecture holds, … See more For two algebraic varieties X and Y, Arapura (2006) has introduced a condition that Y is motivated by X. The precise condition is that the motive of Y is (in André's category of … See more One of the axioms of a Weil theory is the so-called hard Lefschetz theorem (or axiom): Begin with a fixed … See more It is conjectured that the projectors H (X) ↠ H (X) ↣ H (X) are algebraic, i.e. induced by a cycle π ⊂ X × X with rational … See more The Hodge standard conjecture is modelled on the Hodge index theorem. It states the definiteness (positive or negative, according to the dimension) of the cup product … See more Beilinson (2012) has shown that the (conjectural) existence of the so-called motivic t-structure on the triangulated category of motives … See more WebOct 8, 2015 · In 1996, he boosted his international reputation when he solved a conjecture that had been stated by Grothendieck; and in 1998, he gave an invited talk at the International Congress of...
Grothendieck conjecture
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WebFeb 18, 2024 · [Submitted on 18 Feb 2024] The geometrically m-step solvable Grothendieck conjecture for affine hyperbolic curves over finitely generated fields … WebNov 14, 2014 · Mr. Grothendieck’s work was also a steppingstone to solutions of other enigmas famous among mathematicians, but far more arcane. He was instrumental in proving an especially thorny set of...
WebThe Grothendieck conjecture predicts that polynomial relations with coefficients in Φ̄ among the periods of an (algebraic) projective manifold X defined over Φ̄ is … WebOct 17, 2015 · As for 2015, the standard conjectures on algebraic cycles is unconditionally (at lest) known for X: Lefschetz standard conjecture (Grothendieck conjectures A ( X) and B ( X)) a curve (trivial). a surface with H 1 ( X) = 2 ⋅ P i c 0 ( X) (Grothendieck). an abelian variety (Liebermann). a generalized flag manifold G / P …
WebOct 17, 2015 · In "Standard conjectures on algebraic cycles" Grothendieck says: "They would form the basis of the so-called "theory of motives" which is a systematic theory of …
WebThe main topic of this paper is as follows. The origin is due to Grothendieck [Gr66] and its motivic formulation is due to Andr´e [An04] or [An09]: Conjecture 1.1. (Grothendieck’s period conjecture, for simplicity GPC) For any motive M ∈ MM(Q), the point ωM: Spec(C) → Y (M) is a generic point, i.e. the image of ωM is a generic point of ...
WebDec 4, 2007 · The Grothendieck conjecture for affine curves Published online by Cambridge University Press: 04 December 2007 AKIO TAMAGAWA Article Metrics Save … government gateway security questionsWebthe standard conjectures retain their interest for the theory of motives. The first, the Lefschetz standard conjecture (Grothendieck 1969, §3), states that, for a smooth projective variety V over an algebraically closed field, the operators Λ, rendering commutative the diagrams (0 ≤ r≤ 2n, n= dimV) Hr(V) Ln−r −−−−→ ≈ H2n ... government gateway sc2http://www.numdam.org/articles/10.5802/pmb.43/ government gateway sign in ofstedWeb§0. Introduction §1. The Tate Conjecture as a Sort of Grothendieck Conjecture §1.1. The Tate Conjecture for non-CM Elliptic Curves §1.2. Some Pro-p Group Theory §2. Hyperbolic Curves as their own “Anabelian Albanese Varieties” §2.1. A Corollary of the Main Theorem of [Mzk2] §2.2. A Partial Generalization to Finite Characteristic §3. government gateway share codeWebThe “Grothendieck Conjecture” in the title is, in a word, a conjecture to the effect that the arithmetic fundamental group of a hyperbolic algebraic curve completely determines the algebraic structure of the curve. Research concerning this problem was begun at … government gateway sign in pageWebConjecture 1.1 (Grothendieck period conjecture). Let M a Nori motive over Q. Then trdeg Q Q(periods of M) = dimG mot(M): This conjecture is important partly because many interesting numbers arise as pe-riods, such as log2;ˇ. 1.1.3. Andr e’s generalization. While Grothendieck’s conjecture is very general (and children in need assembly videoWebApr 11, 2024 · PDF On Apr 11, 2024, H Behzadipour and others published Research Project No. 7: An Analogue of Knots over Finitely Generated Fields and Grothendieck's Anabelian Philosophy Find, read and cite ... government gateway site login