Dwork conjecture
WebAbstract. The Bombieri-Dwork conjecture predicts that the differential equations satisfied by $G$-functions come from geometry. In this paper, we will look at special ... WebNov 1, 1999 · Introduction In this article, we introduce a systematic new method to investigate the conjectural p-adic meromorphic continuation of Professor Bernard …
Dwork conjecture
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WebIn algebraic geometry, a Dwork family is a one-parameter family of hypersurfaces depending on an integer n, studied by Bernard Dwork.Originally considered by Dwork in … WebDwork’s conjecture on unit root zeta functions By DaqingWan* 1. Introduction In this article, we introduce a systematic new method to investigate the conjectural p-adic meromorphic …
WebJul 1, 2024 · Dwork defined the log-growth Newton polygons of system (1.1) which presents the data of log-growth of all solutions of (1.1) at x = 0 and x = t. Moreover Dwork conjectured the following: Conjecture 1.3 [7, Conjecture 2] The log-growth Newton polygon at x = 0 is above the log-growth Newton polygon at x = t. WebThe Dwork conjecture states that his unit root zeta function is p-adic meromorphic everywhere.[1] This conjecture was proved by Wan .[2][3][4] In mathematics, the Dwork unit root zeta function, named after Bernard Dwork, is the L-function attached to the p-adic Galois representation arising from the p-adic etale cohomology of an algebraic ...
WebDwork’s conjecture grew out of his attempt to understand the p-adic analytic variation of the pure pieces of the zeta function of a variety when the variety moves through an algebraic family. To give an important geometric example, let us con-sider the case that f : Y → X is a smooth and proper morphism over Fq with WebWhether or not I succeeded in doing so - or producing anything novel in the process - I cannot say for sure (probably not), but if it'd be helpful here is a copy: On a Theorem of …
WebLes conjectures de Weil ont largement influencé les géomètres algébristes depuis 1950 ; elles seront prouvées par Bernard Dwork, Alexandre Grothendieck (qui, pour s'y attaquer, mit sur pied un gigantesque programme visant à transférer les techniques de topologie algébrique en théorie des nombres), Michael Artin et enfin Pierre Deligne ...
WebIn the higher rank paper [17], we reduced Dwork’s conjecture from higher rank case over any smooth affine variety Xto the rank one case over the simplest affine space An. In the present paper, we finish our proof by proving the rank one case of Dwork’s conjecture over the affine space An, which is called the key lemma in [17]. hathway dthWebSep 10, 2016 · There is an excellent book by Neal Koblitz "p-adic numbers, p-adic analysis and zeta-functions" were the Dwork's proof is stated in a very detailed way, including all … hathway dth new connectionWebOct 24, 2024 · 1La conjecture de Weil. II. Inst. Hautes Etudes Sci. Publ. Math. No. 52 ... The methods of Dwork are p-adic. For Xa non-singular hypersurface in a projective space they also provided him with a cohomological interpretation of the zeros and poles, and the functional equation. They inspired the crystalline theory of Grothendieck and hathway dth plansWeb2. The Bombieri-Dwork conjecture The Bombieri-Dwork conjecture is an attempt to characterize which differential equations are of geometric origin. Before we introduce this conjecture, let us first look at an interesting example. The Legendre family of elliptic curves is defined by the equation Eλ: y2 = x(x − 1)(x−λ), λ ∈ C− {0,1 ... hathway dth rechargeWebThe Weil conjectures are stated in a paper in 1949. He had earlier proved these conjectures for the case of curves (dv = 1) and Abelian varieties by extending earlier … hathway email idWebSep 23, 2013 · Using Dwork's theory, we prove a broad generalisation of his famous p-adic formal congruences theorem. This enables us to prove certain p-adic congruences for … boots nhs hearing aids pricesWebOct 10, 2015 · In 1949 Weil wrote a ground-breaking article introducing his celebrated conjectures on zeta functions for algebraic varieties of arbitrary dimension, … boots nhs prescription delivery