Grothendieck section conjecture
WebThe Grothendieck conjecture predicts that polynomial relations with coefficients in Φ̄ among the periods of an (algebraic) projective manifold X defined over Φ̄ is determined by the Hodge cycles on the powers of X Φ̄ (or by the algebraic cycles, in the strongest version). WebDec 4, 2007 · A combinatorial version of the Grothendieck conjecture. Tohoku Mathematical Journal, Vol. 59, Issue. 3, ... Packets in Grothendieck's section conjecture. Advances in Mathematics, Vol. 218, Issue. 2, p. 395. CrossRef; Google Scholar; Corry, Scott and Pop, Florian 2009. The pro-p Hom-form of the birational anabelian conjecture. …
Grothendieck section conjecture
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WebApr 19, 2024 · Abstract: Grothendieck gave two forms of his "main conjecture of anabelian geometry", i.e. the section conjecture and the hom conjecture. He stated that these … WebThe Weil conjectures are now known to be true (by work of Alexandre Grothendieck, Michael Artin, Pierre Deligne, et al). This course will provide an overview of the methods and ideas which have led to the formulation and the proof of the Weil conjectures. In particular, we hope to cover
WebConjecture 1.1 (The section conjecture). Let kbe a number field or a p-adic field, and let X/kbe a smooth, projective, geometrically connected curve of genus ≥2. Then the map hX/k is a bijection. It is thought that Grothendieck’s reason for this conjecture is topological, and In anabelian geometry, a branch of algebraic geometry, the section conjecture gives a conjectural description of the splittings of the group homomorphism , where is a complete smooth curve of genus at least 2 over a field that is finitely generated over , in terms of decomposition groups of rational points of . The conjecture was introduced by Alexander Grothendieck (1997) in a 1983 letter to Gerd Faltings.
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, envisaged by Alexander Grothendieck, was to prove that his construction of pure motives gave an abelian category that is semisimple. Moreover, as he pointed out, the standard conjectures also imply the hardest part of the Weil conjectures, namely the "Riemann h… WebThe conjecture of Kontsevich–Zagier is remarkable in its simplicity as it can be stated in elementary terms. However, in practice, the conjec-ture of Grothendieck is better suited for deducing algebraic independence of periods. 1.4 The geometric version As it is the case with many deep and di cult prob-lems on numbers, the conjectures of ...
WebConjecture 2.2 (Grothendieck’s section conjecture). Let U be a hyperbolic curve defined over a field k of finite type over Q. Then (SC1) The map U(k)→Hom-extΓ …
WebConjecture (Grothendieck, "Hom conjecture"). Let k be finitely generated over Q. If T/k is a smooth variety and X/k is a smooth, proper anabelian variety, then Homk(T,X)→Hom … north bend oregon motelWebThe Grothendieck conjecture for affine curves AKIO TAMAGAWA Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-01, Japan ... exists or not, so the formalism in Section 2 remains to be a mere formalism, for the present. (See the end of Section 2.) In Section 4, we give the proof of Theorems ... how to replace sesame oilWebMay 15, 2003 · The section conjecture in Grothendieck’s anabelian geometry says that the sections of the canonical projection π 1 (X ) ↠ GK are (up to conjugation) in one-to … north bend oregon to bandon oregonWebRequest PDF On Grothendieck's section conjecture for orbicurves As already noted by Niels Borne and Michel Emsalem, there is a natural generalization of the section conjecture for proper ... north bend oregon storage unitsWebIn mathematics, the Grothendieck–Katz p-curvature conjecture is a local-global principle for linear ordinary differential equations, related to differential Galois theory and in … north bend oregon movie theater scheduleWebGrothendieck’s standard conjectures By J. S. Milne* Abstract We prove that Grothendieck’s Hodge standard conjecture holds for abelian varieties in arbitrary … north bend oregon to eugene oregonWebTheorem 1 (Borel, Grothendieck, Landman). T is a quasi-unipotent matrix, i.e. the eigenvalues of T are roots of unity. We indicate Grothendieck’s proof since it seems the most relevant here. First, we need to make a switch to a more algebraic picture. We replace with the spectrum Sof Henselian1 discrete valuation ring R. Let k= R=mbe the residue north bend oregon veterinary clinics