P adic height pairing

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August undefined, 2024

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. Webp-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 …

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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 … Webp-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. … dr lynda youngworth

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WebDec 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 ... 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 dr lyndly tamura

Height pairings on Shimura curves and p-adic uniformization

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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 ... 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 dr lynda yang university of michiganWebRemark 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. dr lynda newman montford specialist centre

"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 … " - P adic height pairing

P adic height pairing

COLEMAN-GROSS HEIGHT PAIRINGS AND THE p-ADIC …

WebIn 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 … WebThe p-adic height pairing 16 4. An exact sequence 19 5. Proof of Theorem B 25 References 28 1. Introduction Let F be a number ﬁeld with ring of integers O F. Suppose that E/O F is an abelian scheme of dimension d, and that p>2 is a rational prime. In this

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Web2.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 … 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

Web5. p-adic height pairings II: universal norms 71 5.1. The pairing hnorm V,D 71 5.2. Comparision with hsel V,D 76 6. p-adic height pairings III: splitting of local extensions 80 6.1. The pairing hspl V,D 80 6.2. Comparision with Nekováˇr’s height pairing 83 6.3. Comparision with hnorm V,D 85 7. p-adic height pairings IV: extended Selmer ... WebThe p -adic analogue [ 20] of the BSD conjecture makes a similar prediction, with the canonical height pairing replaced by a p -adic one [ 19 ]. These conjectures have natural generalizations to abelian varieties. The p -adic height pairing was first defined by Schneider [ 24] for abelian varieties and was extended to motives by Nekovář [ 23 ].

WebNov 12, 2014 · The theory of the p-adic valued height pairing on abelian varieties was developed in the 1980s by Néron, Zarhin, Schneider, Mazur-Tate, etc. Compared with the real valued Néron-Tate height pairing, one important aspect in the p-adic valued case is that the pairing depends on several choices and in this sense there is no canonical p-adic height … WebFeb 28, 2012 · In this paper we give an alternative definition of the p-adic height pairing and prove a generalization of Rubin's result, relating the derived heights to higher derivatives …

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 …

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 … col brian cliffordhttp://math.bu.edu/people/rpollack/Papers/2024_10_Critical_GZ-I.pdf dr lynda thomas-mabineWebSummary. In the first section of his seminal paper on height pairings, Beilinson constructed an ℓ -adic height pairing for rational Chow groups of homologically trivial cycles of complementary codimension on smooth proper varieties over the function field of a curve over an algebraically closed field, and asked about a generalization to ... col brendan o\\u0027sheaWebp-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. col brent tothWebOn p-adic height pairings Jan Nekov a r The aim of the present work is to construct p-adic height pairings in a su ciently general setting, namely for Selmer groups of reasonably behaved p-adic Galois representations over number elds. These pairings should, modulo … col brent parkerWebThe local height pairing at v p of Coleman and Gross is deﬁned as follows: Let y and z be two divisors of degree 0 on X with disjoint supports. Then their pairing is given by h v col brewsterWeb3.3. 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. dr lyndon bouah