Grothendieck section conjecture

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August undefined, 2024

WebGROTHENDIECK’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 … 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

Basics on anabelian geometry and Grothendieck

WebNov 10, 2024 · The Grothendieck Period Conjecture has been formulated and proved by Ayoub and Nori. We shall explain the geometric analogue of the André - Grothendieck … 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. downtown la crosse wi map

The section conjecture at the boundary of moduli space

Webplying Stokes’ theorem. The two are related by a conjecture of Grothendieck (see [11] for more history and discussion) which is phrased more generally for motives, but for the purposes of the above discussion we may take M= Hp(X) for a variety Xde ned over Q: Conjecture 1.1 (Grothendieck period conjecture). Let M a Nori motive over Q. Then trdeg WebJul 6, 2024 · We formulate a tropical analogue of Grothendieck’s section conjecture: that for every stable graph Γ of genus g>2, and every field k, the generic curve with reduction type Γ over k satisfies ... WebJan 1, 2011 · We survey topics related to étale fundamental groups, with emphasis on Grothendieck’s anabelian program, the Section Conjecture and Parshin’s proof of the … downtown la cycling classes

Version of the Grothendieck Conjecture for p-adic Local Fields

Math 608R: Etale Cohomology and the Weil conjectures - UMD

WebThe goal of this article is to show a part of Grothendieck's section conjecture using the identification of sections with neutral fiber functors as defined in [H. Esnault, P.H. Hai, The ... WebarXiv:math/0603095v1 [math.KT] 3 Mar 2006 SMOOTH K-THEORY OF LOCALLY CONVEX ALGEBRAS H. INASSARIDZE AND T. KANDELAKI Abstract. Smooth K-functors are introduced and the smooth clean furry artWebThe Grothendieck conjecture for afﬁne curves AKIO TAMAGAWA Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-01, Japan e-mail: … clean furry pics

"WebJul 23, 2012 · Section Conjecture. — (Grothendieck) Let Xbe a smooth, compact algebraic curve of genus 2deﬁned over a number ﬁeld k. Then Map(Speck;X) ! … " - Grothendieck section conjecture

Grothendieck section conjecture

[0911.3309] Notes on the section conjecture of Grothendieck

WebIn mathematics, the Grothendieck–Katz p-curvature conjecture is a local-global principle for linear ordinary differential equations, related to differential Galois theory and in … WebJun 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 …

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WebMay 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 … WebNov 17, 2009 · Download a PDF of the paper titled Notes on the section conjecture of Grothendieck, by Feng-Wen An. Download PDF Abstract: In this short note, we will give the key point of the section conjecture of Grothendieck, that is reformulated by monodromy actions. Here, we will also give the result of the section conjecture for algebraic …

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 ... 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…

WebGiven a group, we construct a fundamental additive functor on its orbit category. We prove that any isomorphism conjecture valid for this fundamental additive functor holds for all additive functors, like -theory, cycl… WebThe tropical section conjecture is true for some stable graphs Theorem (Li, Litt, Salter, S.) Letk beacharacteristic0ﬁeld. Thetropicalsectionconjectureis trueforthefollowinggraphs. Forg ¥3,letH g bethestablegraphconsistingofa g 1-cycle,allofwhoseverticeshavegenus1. Thesequenceˇ 1-ab-seqpC g;zK Hg qdoesnotsplitforH g. Forg ¥2even,letT

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).

WebTheorem 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 downtown la crosse wi barsWebThe section conjecture in Grothendieck's anabelian geometry says that the sections of the canonical projection from the arithmetic fundamental group of X onto the absolute … clean furry comicsWebConjecture 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 … downtown la delivery foodWebof the Grothendieck conjecture (resp.the Hom version of the Grothendieck conjecture; the Grothendieck section conjecture). Suppose that Xis a hyperbolic curve. In the case where Kis ﬁnitely generated over Q, Y is also a hyperbolic curve, and at least one of Xand Y is aﬃne, Question 0.1.1 was aﬃrmatively answered by Tamagawa [13]. cleanfuseWebApr 3, 2024 · Grothendieck's section conjecture predicts that over arithmetically interesting fields (e.g. number fields or p-adic fields), rational points on a smooth projective curve X of genus at least 2 can be detected via the … clean furry imagesWebConjecture 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 cleanfusetmWebof the Grothendieck conjecture (resp.the Hom version of the Grothendieck conjecture; the Grothendieck section conjecture). Suppose that Xis a hyperbolic curve. In the … clean furry