P adic height pairing

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WebJun 9, 2004 · The intersection pairing in an extension of the p-adic height pairing for divisors of degree 0 in the form described by Coleman and Gross. It also uses Coleman integration and is related to work ... Webp-adic height pairing takes values in cycl Z p. By work of Cornut [5] and Vatsal [21] we know that Uis free of rank one over . This implies that the image of the cyclotomic p-adic height pairing is generated by an element R2 cycl Z p, the -adic regulator of E. Our main motivation for this paper was to compute examples of the -adic regulator of E.

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WebHeight pairings on Shimura curves and p-adic uniformization 155. method is due to Genestier, [8]. His crucial observation is that Z(j)may be identiﬁed with the ﬁxed point … WebHere is the formula for the cyclotomic p-adic height of P, i.e., the value of hp(P) := − 1 2 (P,P)p ∈ Qp where ( , )p is the height pairing attached to GQ → Qp, the cyclotomic linear … stanley bunk beds young america

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Webp -adic height pairings. II Peter Schneider Inventiones mathematicae 79 , 329–374 ( 1985) Cite this article 375 Accesses 71 Citations Metrics Download to read the full article text … WebRemark 1.2. Height pairings attached to other p-adic linear functionals can be degenerate; in fact, given an elliptic curve deﬁned over Q with good ordinary reduction at p, and K a quadratic imaginary ﬁeld over which the Mordell-Weil group E(K) is of odd rank, the p-adic anticyclotomic height pairing for E over K is always degenerate. Web3.3. A -adic cyclotomic height pairings 15 3.4. Specializations and comparison with Nekov a r’s heights 16 3.5. Universal Heegner points 19 4. p-adic L-functions over the imaginary quadratic eld K 21 4.1. Ranking-Selberg p-adic L-functions 21 4.2. Na ve p-adic L-functions over K 23 4.3. A factorization formula 24 Key words and phrases. perth best seafood restaurants

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WebDec 23, 2016 · The non-degeneracy of the canonical p-adic height pairing defined by Perrin-Riou and Schneider on an elliptic curve over a number field with good, ordinary reduction … WebOct 27, 2024 · We formulate a p-adic analogue of the Arithmetic Gan--Gross--Prasad conjecture for unitary groups, relating the p-adic height pairing of the arithmetic diagonal … perth beta bomWeb2.The height pairing on CH R is non-degenerate. 3.Its determinant, times the determinant of the (real) period matrix for H2i 1(X), equals the ... Let Kbe a p-adic eld, Xa smooth proper … stanley bunk bed with trundle

"WebOne of the puzzling features of the anticyclotomic setting is the presence of predictable degeneracies in the associated height pairings. (In the cyclotomic case, a conjecture of Mazur predicts that the cyclotomic p-adic height pairing is always non-degenerate.) Such degeneracies lead to extra vanishing of the corresponding p-adic L-functions. " - P adic height pairing

P adic height pairing

WebOct 1, 2024 · The extended Coleman-Gross height pairing, still denoted h CG, is defined exactly at the usual Coleman-Gross height pairing, but using Vologodsky integration … WebIn this paper, we will present a new construction of the p-adic height pairings of Mazur-Tate [MT] and Schneider [S], when the Abelian variety in question is the Jacobian of a curve. …

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WebHe formulated a conjecture under which a commuting pair of series should arise from a formal group. Using methods from p-adic Hodge theory, we prove the height one case of this conjecture. ... The p-adic upper half plane comes equipped with a remarkable tower of GL(2)-equivariant etale covering spaces, as was shown by Drinfeld. ... WebGross height pairing with the p-adic height deﬁned via bi-extensions as in [MT83], or by the work of the second author [Bes04] tying it with the general height pairing deﬁned by Nekov´aˇr [Nek93]. This proof is ultimately global in nature, even though both heights are sums of local terms.

WebOct 27, 2024 · We formulate a p-adic analogue of the Arithmetic Gan--Gross--Prasad conjecture for unitary groups, relating the p-adic height pairing of the arithmetic diagonal cycles to the first central derivative (along the cyclotomic direction) of a p-adic Rankin—Selberg L-function associated to cuspidal automorphic representations. http://math.stanford.edu/~conrad/BSDseminar/Notes/L16.pdf

WebFor the purpose of numerically verifying p -adic BSD-type conjectures, it is important to have an effective algorithm for the computation of the p -adic height pairing. By the work of … WebHis doctoral thesis there was supervised by Glenn H. Stevens; the thesis title is p-adic Cohomology of Abelian Varieties. Career As a ... Iovita, Adrian; Werner, Annette (2003). "p-adic height pairings on abelian varieties with semistable ordinary reduction". Journal für die reine und angewandte Mathematik. 2003 (564): 181–203.

WebThe algebraic p-adic height pairing In this section we shall describe the algebraic p-adic height pairing on E=F. The reader may refer to section 3 of [PR1] or to chapter IV of [PR2] for full details of the results we use. We begin by recalling various elementary facts about Selmer groups. If q is a

WebThis global p-adic height pairing can, in turn, be decomposed into a sum of local height pairings at each prime. In particular, for C a hyperelliptic curve over Qp with pa prime of good reduction and for D 1,D 2∈ Div0(C) with disjoint support, the Coleman-Gross p-adic height pairing at pis given in terms of the Coleman integral [10] hp(D 1,D 2) = Z stanley bunsick orthodontistWebDec 22, 2014 · A new duality formalism is developed, which leads to generalized Cassels-Tate pairings and generalized p-adic height pairings. One of the applications is a parity result for Selmer groups ... stanley busy busy octopus-honest ostrichWebp-adic height pairing should be true, just as it is for the real-valued N´eron–Tate height. In particular, the p-adic height of a non-torsion point on an elliptic curve of rank one should … perth best restaurants 2022Webp-adic height pairing at the prime p is given in terms of the Coleman integral hp(D1,D2) = Z D2 ωD1, for an appropriately constructed diﬀerential ωD1 associated to the divisor D1. … stanley burnside primary school dh9WebOct 1, 2024 · On p-adic height pairings. Séminaire de Théorie des Nombres, Progr. Math., vol. 108, Paris, 1990–91, Birkhäuser Boston, Boston, MA (1993), pp. 127-202, 10.1007/s10107-005-0696-y. View in Scopus Google Scholar [23] V. Vologodsky. Hodge structure on the fundamental group and its application to p-adic integration. perth best western hotelWebp(f) are the determinants of the complex and the p-adic height pairings computed in the same basis. If r = 1; this question is closely related to p- adic analogues of the Gross … stanley burford artistWebIn this section we present a simple geometric construction for the height pairing (and hence a solution of Conjecture 1.3) in the case where the K-variety X admits a smooth proper … stanley burgers central falls ri