Grothendieck section conjecture
WebFeb 8, 2024 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site WebApr 13, 2024 · Abstract: A lot of the algebraic and arithmetic information of a curve is contained in its interaction with the Galois group. This draws inspiration from topology, where given a family of curves over a base B, the fundamental group of B acts on the cohomology of the fiber. As an arithmetic analogue, given an algebraic curve C defined …
Grothendieck section conjecture
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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). WebWhen applied to Grothendieck section conjecture, it allows us to find a k-structure on the universal covering, and k-rational pro-points at finite and infinite distance which lift given k-rational points. 1.
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 … WebJan 19, 2024 · Grothendieck’s fundamental short exact sequenceof profinite groups(SGA1), is: 1→π1(X¯)→π1(X)→Γk→1.1 \to\pi_1 (\overline{X})\to\pi_1 (X) \to …
WebThe 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 ... WebApr 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 ...
WebThe starting point for this work is Grothendieck’s section conjecture, which suggests that in many cases the sequence above encodes all of the arithmetic of X: Conjecture 1.1.2 (The section conjecture [Gro97]). Suppose kis a nitely-generated eld of characteristic 0 and that the genus of Xis at least 2. Then the map
WebThese Grothendieck conjectures were partially solved by Hiroaki Nakamura and Akio Tamagawa, while complete proofs were given by Shinichi Mochizuki. Anabelian … credit cards chip waterproofWebJun 22, 2014 · Are there any good references which explain the injectivity part of Grothendieck's section conjecture in details? I heard that Grothendieck himself gave a … credit card schemaWebJun 30, 2024 · This conjecture may be seen as a sort of compromise between the abelian confines of the BSD conjecture and the profinite world of the Grothendieck section conjecture. After stating the conjecture and explaining its relationship to these other conjectures, we explore a range of special cases in which the new conjecture can be … buckingham estates overland park ks hoa loginWebSOME IMPLICATIONS BETWEEN GROTHENDIECK’S ANABELIAN CONJECTURES 3 The name "printable" is meant to suggest that ΠX/k "prints" X, similarly to how an algebraic space represents a sheaf. For smooth, proper, hyperbolic curves over a field k finitely generated over Q, printability is equivalent to the section conjecture over all finitely … credit cards check my creditWebWhat does the Grothendieck's period conjecture mean? I would like to know how is the Grothendieck's period conjecture about algebraic cycles, defined explicitly ? and, what … buckingham family practice paWebNov 5, 2011 · We establish a valuative version of Grothendieck's section conjecture for curves over p-adic local fields. The image of every section is contained in the decomposition subgroup of a valuation which prolongs the p-adic valuation to the function field of the curve. buckingham family practice doctorsWebGROTHENDIECK’S PERIOD CONJECTURE FOR KUMMER SURFACES OF SELF-PRODUCT CM TYPE DAIKI KAWABE Abstract. We show that Grothendieck’s period conjecture holds for the Kummer ... In section 3, we prove our main theorem. 2. Grothendieck’s period conjecture 2.1. Motivic Galois groups. We can define the … buckingham farms