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Algebraic number theory and code design for Rayleigh fading channels [PDF]

open access: green, 2004
Algebraic number theory is having an increasing impact in code design for many different coding applications, such as single antenna fading channels and more recently, MIMO systems.
Oggier, F., Viterbo, E.
core   +4 more sources

Quantum algorithms for problems in number theory, algebraic geometry, and group theory [PDF]

open access: green, 2012
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same problem ...
Sasaki, Yoshitaka, van Dam, Wim
core   +2 more sources

Trace formalism for motivic cohomology [PDF]

open access: yesÉpijournal de Géométrie Algébrique, 2023
The goal of this paper is to construct trace maps for the six functor formalism of motivic cohomology after Voevodsky, Ayoub, and Cisinski-D\'{e}glise. We also construct an $\infty$-enhancement of such a trace formalism.
Tomoyuki Abe
doaj   +1 more source

Density of Arithmetic Representations of Function Fields [PDF]

open access: yesÉpijournal de Géométrie Algébrique, 2022
We propose a conjecture on the density of arithmetic points in the deformation space of representations of the \'etale fundamental group in positive characteristic. This?
Hélène Esnault, Moritz Kerz
doaj   +1 more source

Etale and crystalline companions, I [PDF]

open access: yesÉpijournal de Géométrie Algébrique, 2022
Let $X$ be a smooth scheme over a finite field of characteristic $p$. Consider the coefficient objects of locally constant rank on $X$ in $\ell$-adic Weil cohomology: these are lisse Weil sheaves in \'etale cohomology when $\ell \neq p$, and ...
Kiran S. Kedlaya
doaj   +1 more source

On simple modules with singular highest weights for so2l+1(K) [PDF]

open access: yesҚарағанды университетінің хабаршысы. Математика сериясы, 2022
In this paper, we study formal characters of simple modules with singular highest weights over classical Lie algebras of type B over an algebraically closed field of characteristic p ≥ h, where h is the Coxeter number. Assume that the highest weights of
Sh.Sh. Ibraev   +2 more
doaj   +2 more sources

Optimal Ate Pairing on Elliptic Curves with Embedding Degree $9,15$ and $27$ [PDF]

open access: yesGroups, Complexity, Cryptology, 2020
Much attention has been given to the efficient computation of pairings on elliptic curves with even embedding degree since the advent of pairing-based cryptography.
Emmanuel Fouotsa   +2 more
doaj   +1 more source

N\'eron models of Jacobians over bases of arbitrary dimension [PDF]

open access: yesÉpijournal de Géométrie Algébrique, 2022
We work with a smooth relative curve $X_U/U$ with nodal reduction over an excellent and locally factorial scheme $S$. We show that blowing up a nodal model of $X_U$ in the ideal sheaf of a section yields a new nodal model, and describe how these models ...
Thibault Poiret
doaj   +1 more source

Algebraic, Analytic, and Computational Number Theory and Its Applications

open access: yesMathematics, 2023
Analytic number theory is a branch of number theory which inherits methods from mathematical analysis in order to solve difficult problems about the integers [...]
Diana Savin   +2 more
doaj   +1 more source

Finiteness of cohomology groups of stacks of shtukas as modules over Hecke algebras, and applications [PDF]

open access: yesÉpijournal de Géométrie Algébrique, 2020
In this paper we prove that the cohomology groups with compact support of stacks of shtukas are modules of finite type over a Hecke algebra. As an application, we extend the construction of excursion operators, defined by V.
Cong Xue
doaj   +1 more source

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