ON THE DISTRIBUTION OF GALOIS GROUPS

On the Distribution of Galois Groups, II

On the Galois Structure of Selmer Groups

Let A be an abelian variety defined over a number field k and F a finite Galois extension of k. Let p be a prime number. Then under certain not-too-stringent conditions on A and F we investigate the explicit Galois structure of the p-primary Selmer group of A over F . We also use the results so obtained to derive new bounds on the growth of the Selmer rank of A over extensions of k.

Galois Action on Class Groups

It is well known that the Galois group of an extension L/F puts constraints on the structure of the relative ideal class group Cl(L/F ). Explicit results, however, hardly ever go beyond the semisimple abelian case, where L/F is abelian (in general cyclic) and where (L : F ) and #Cl(L/F ) are coprime. Using only basic parts of the theory of group representations, we give a unified approach to th...

survey on the rule of the due & hindering relying on the sheikh ansaris ideas

قاعده مقتضی و مانع در متون فقهی کم و بیش مستند احکام قرار گرفته و مورد مناقشه فقهاء و اصولیین می باشد و مشهور معتقند مقتضی و مانع، قاعده نیست بلکه یکی از مسائل ذیل استصحاب است لذا نگارنده بر آن شد تا پیرامون این قاعده پژوهش جامعی انجام دهد. به عقیده ما مقتضی دارای حیثیت مستقلی است و هر گاه می گوییم مقتضی احراز شد یعنی با ماهیت مستقل خودش محرز گشته و قطعا اقتضاء خود را خواهد داشت مانند نکاح که ...

The Determination of Galois Groups

A technique is described for the nontentative computer determination of the Galois groups of irreducible polynomials with integer coefficients. The technique for a given polynomial involves finding high-precision approximations to the roots of the polynomial, and fixing an ordering for these roots. The roots are then used to create resolvent polynomials of relatively small degree, the linear fa...