Results 11 to 20 of about 93,960,166 (81)

Root numbers and parity phenomena

Bulletin of the London Mathematical Society, Volume 55, Issue 6, Page 2557-2597, December 2023., 2023
Abstract The parity conjecture has a long and distinguished history. It gives a way of predicting the existence of points of infinite order on elliptic curves without having to construct them, and is responsible for a wide range of unexplained arithmetic phenomena.
Lilybelle Cowland Kellock, Vladimir Dokchitser   +1 more
wiley   +1 more source

Monodromy of subrepresentations and irreducibility of low degree automorphic Galois representations

Journal of the London Mathematical Society, Volume 108, Issue 6, Page 2436-2490, December 2023., 2023
Abstract Let X$X$ be a smooth, separated, geometrically connected scheme defined over a number field K$K$ and {ρλ:π1(X)→GLn(Eλ)}λ$\lbrace \rho _\lambda :\pi _1(X)\rightarrow \mathrm{GL}_n(E_\lambda )\rbrace _\lambda$ a system of semisimple λ$\lambda$‐adic representations of the étale fundamental group of X$X$ such that for each closed point x$x$ of X$X$
Chun Yin Hui
wiley   +1 more source

The geometric interpretation of the Tate pairing and its applications [PDF]

, 2023
While the Weil pairing is geometric, the Tate pairing is arithmetic: its value depends on the base field considered. Nevertheless, the étale topology allows to interpret the Galois action in a geometric manner.
Damien Robert
core   +1 more source

Algebraic theories of power operations

Journal of Topology, Volume 16, Issue 4, Page 1543-1640, December 2023., 2023
Abstract We develop and exposit some general algebra useful for working with certain algebraic structures that arise in stable homotopy theory, such as those encoding well‐behaved theories of power operations for E∞$\mathbb {E}_\infty$ ring spectra.
William Balderrama
wiley   +1 more source

Descent Via Isogeny on Elliptic Curves with Large Rational Torsion Subgroups. [PDF]

, 2008
We outline PARI programs which assist with various algorithms related to descent via isogeny on elliptic curves. We describe, in this context, variations of standard inequalities which aid the computation of members of the Tate-Shafarevich group.
Flynn, Eugene, Flynn, E. V., Flynn, EV, E.V. Flynn, Grattoni, C, C. Grattoni, Grattoni, C., Flynn, E.V.   +7 more
core   +1 more source

Besides Looking: Patrimony, Perfomativity and Visual Cultures [PDF]

, 2008
David Dibosa’s paper, 'Besides Looking: Patrimony, Performativity and Visual Cultures in National Art Museums', is an exploration and a further elaboration of the relations between the development of visual media practices within the research – what we ...
Dibosa, David
core   +5 more sources

On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field [PDF]

, 2013
In this note, we consider the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field. P. Bruin [1] defined this pairing over finite field k: ker ˆφ(k) × coker(φ(k)) ⟶ k∗, and proved its perfectness over finite field.
Nesteruk, V.
core   +1 more source

Efficient algorithms for pairing-based cryptosystems [PDF]

, 2002
We describe fast new algorithms to implement recent cryptosystems based on the Tate pairing. In particular, our techniques improve pairing evaluation speed by a factor of about 55 compared to previously known methods in characteristic 3, and attain ...
B. Lynn, H. Kim, Hae Y. Kim, Barreto, Paulo S.L.M., Paulo S. L. M. Barreto, Scott, Michael, Michael Scott, Kim, Hae Y., M. Scott., Hae Y. Kim, Lynn, Ben, P. Barreto, Ben Lynn, Paulo S. L. M. Barreto   +13 more
core   +1 more source

Computing the Cassels–Tate pairing on 3-isogeny Selmer groups via cubic norm equations [PDF]

, 2018
We explain a method for computing the Cassels-Tate pairing on the 3-isogeny Selmer groups of an elliptic curve. This improves the upper bound on the rank of the elliptic curve coming from a descent by 3-isogeny, to that coming from a full 3-descent.

core   +2 more sources

On 7‐adic Galois representations for elliptic curves over Q$\mathbb {Q}$

Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.
Abstract In recent years, significant progress has been made on Mazur's Program B, with many authors beginning a systematic classification of all possible images of p$p$‐adic Galois representations attached to elliptic curves over Q$\mathbb {Q}$. Currently, the classification is only complete for p∈{2,3,13,17}$p \in \lbrace 2,3,13,17\rbrace$.
Lorenzo Furio, Davide Lombardo
wiley   +1 more source