The abelian part of a compatible system and $$\ell $$ℓ-independence of the Tate conjecture

In his 1982 paper, Ogus defined a class of cycles in the de Rham cohomology of smooth proper varieties over number fields. This notion is a crystalline analogue of$\ell$-adic Tate cycles. In the case of abelian varieties, this class includes all the Hodge cycles by the work of Deligne, Ogus, and Blasius. Ogus predicted that such cycles coincide with Hodge cycles for abelian varieties. In this paper, we confirm Ogus’ prediction for some families of abelian varieties. These families include geometrically simple abelian varieties of prime dimension that have non-trivial endomorphism ring. The proof uses a crystalline analogue of Faltings’ isogeny theorem due to Bost and the known cases of the Mumford–Tate conjecture.

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Compatible System for Predicting Total and Merchantable Stem Volume over and under Bark, Branch Volume and Whole-Tree Volume of Pine Species

Forests ◽

10.3390/f8110417 ◽

2017 ◽

Vol 8 (11) ◽

pp. 417 ◽

Cited By ~ 8

Author(s):

José Corral-Rivas ◽

Daniel Vega-Nieva ◽

Roque Rodríguez-Soalleiro ◽

Carlos López-Sánchez ◽

Christian Wehenkel ◽

...

Keyword(s):

Stem Volume ◽

Compatible System ◽

Whole Tree ◽

Pine Species

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The Hodge conjecture and the Tate conjecture for fermat varieties

Proceedings of the Japan Academy Series A Mathematical Sciences ◽

10.3792/pjaa.55.111 ◽

1979 ◽

Vol 55 (3) ◽

pp. 111-114 ◽

Cited By ~ 10

Author(s):

Tetsuji Shioda

Keyword(s):

Hodge Conjecture ◽

Tate Conjecture

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ON SELMER RANK PARITY OF TWISTS

Journal of the Australian Mathematical Society ◽

10.1017/s1446788716000306 ◽

2016 ◽

Vol 102 (3) ◽

pp. 316-330 ◽

Cited By ~ 1

Author(s):

MAJID HADIAN ◽

MATTHEW WEIDNER

Keyword(s):

Elliptic Curves ◽

Abelian Variety ◽

Number Field ◽

Arbitrary Number ◽

Hyperelliptic Curve ◽

Abelian Varieties ◽

Hyperelliptic Curves ◽

Torsion Subgroup ◽

Tate Conjecture ◽

Quadratic Twists

In this paper we study the variation of the $p$-Selmer rank parities of $p$-twists of a principally polarized Abelian variety over an arbitrary number field $K$ and show, under certain assumptions, that this parity is periodic with an explicit period. Our result applies in particular to principally polarized Abelian varieties with full $K$-rational $p$-torsion subgroup, arbitrary elliptic curves, and Jacobians of hyperelliptic curves. Assuming the Shafarevich–Tate conjecture, our result allows one to classify the rank parities of all quadratic twists of an elliptic or hyperelliptic curve after a finite calculation.

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On the Sato-Tate conjecture for QM-curves of genus two

Mathematics of Computation ◽

10.1090/s0025-5718-99-01061-3 ◽

1999 ◽

Vol 68 (228) ◽

pp. 1649-1663 ◽

Cited By ~ 2

Author(s):

Ki-ichiro Hashimoto ◽

Hiroshi Tsunogai

Keyword(s):

Tate Conjecture ◽

Genus Two

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Permissible Medicine and Rationalization of Halal Pharma

Halalpshere ◽

10.31436/hs.v1i1.18 ◽

2021 ◽

Vol 1 (1) ◽

pp. 43-52

Author(s):

Jawad Alzeer

Keyword(s):

Potential Energy ◽

Production Process ◽

Placebo Effect ◽

Therapeutic Drug ◽

Spiritual Values ◽

Therapeutic Concept ◽

Compatible System ◽

Specific Standard ◽

The Right

Permissible medicine “Halalopathy” represents a compatible relation between therapeutic drug and human beliefs/lifestyles. Production of permissible drugs is achieved by evaluating ingredients and monitoring the production process to be compatible with a certain specific standard depending on the requirement of the lifestyle or belief of the patient. If drugs and beliefs are compatible, a domino chain effect will be initiated; trust will be developed, and the placebo effect will be activated. Consequently, a compatible system between mind and drug is established, faith in the treatment is intensified, entropy is lowered, potential energy is increased, and self-assurance is enriched. The compatibility concept is based on finding a connection between human’s belief and therapeutic drug where certain genes will be turned off epigenetically. Halalopathic medicine represents a new therapeutic concept in which holistic values - material, human, moral and spiritual values - are used to deliver the right treatment to the right patient.

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