The commutative pseudo-reductive groups admit no useful classification ( in contrast with the reductive case, for which they are tori and hence are accessible via Galois lattices ), but modulo this one has a useful description of the situation away from characteristics 2 and 3 in terms of reductive groups over some finite extensions of the ground field.
42.
7 ) In elliptic curve cryptography, the Weil descent attack uses the Weil restriction to transform a discrete logarithm problem on an elliptic curve over a finite extension field L / K, into a discrete log problem on the Jacobian variety of a hyperelliptic curve over the base field K, that is potentially easier to solve because of K's smaller size.
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J pointed out, such a definition is vacuous . ( And, if I understand correctly, if we require a Galois group to be profinite and further assume that there is a Galois connection, then it would follow that the extension is algebraic ( since the union of finite extensions is algebraic . )-- talk ) 02 : 23, 4 February 2010 ( UTC)
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Simply cutting the sine function after some finite extension and setting the wavefunction to zero outside of that " box " doesn't solve the problem bacause you introduce other wavelegths into the fourier analysis of that modified wavefunction other than the original wavelength . In other words, you pay for your partial determination of the position of the particle with uncertainty about the wavelength ( and momentum ).
45.
Vladimir Berkovich reformulated much of the theory of rigid analytic spaces in the late 1980s, using a generalization of the notion of Gelfand spectrum for commutative unital Bruhat & ndash; Tits buildings for " PGL " 2 ( " F " ), as " F " varies over finite extensions of "'Q " "'p ", when the buildings are given a suitably coarse topology.
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