By Bandini A.

Show description

Read Online or Download 3-Selmer groups for curves y^2 = x^3 + a PDF

Similar symmetry and group books

Download e-book for iPad: Perfect Symmetry. The Search for the Beginning of Time by Heinz R.

Well known technology at its most sensible, this acclaimed vintage paintings describes in gorgeous aspect how state of the art discoveries in quantum physics and cosmology are assisting to provide an explanation for the beginning and evolution of the universe, of area and time. excellent Symmetry is an confident file in regards to the ongoing synthesis of those disciplines right into a concerted attempt to discover the basic legislation that not just describe how the stuff that makes up the universe -- topic and effort -- got here into life but in addition govern the habit of the smallest and biggest issues, from subatomic debris to stars, galaxies, and the universe itself.

Additional resources for 3-Selmer groups for curves y^2 = x^3 + a

Sample text

K[C ]-module i f Iker V is faithful, and from step 4 we know that Suppose that Icl. is faithful. From step 6 we know that that char k = p By is faithful. _-- = e/ker v. Ic I, ul G• is isomorphic with a direct summand of is algebraic. We conclude that V Step 8. V PE. is an VI G0 . is is a direct is algebraic, = PE. acts trivially on By step 7, V and - 47 - 1. C (E) therefore We now have shown that Z(G). El Thus (1)-(3) all P hold. 6)(d), vity of implies that every normal abelian subgroup of E structure of E the fonn primiti- P P is cyclic.

9), "K is a finite extension field of K. By the Wedderburn structure theorems for siluple algebras, where K is the center of A ces an antiautomorphism a oE ([CRI] SectLon 3n). A ~~ow we see that C\ indu- satisEying properties (i) and (iii). - 54 - Suppose x EG has image x in A and a E K, the center of A. Then (since a is an antiautomorphism) "- is an automorphism of (t so that all( = ~ + a I) = then + t I = o + I The proposition holds. = H0"'K A We now compute in the algebra we t E K Clearly, if ~ aj proving (il) .

C_ g. K[N]- isomorphism of \,v into - 60 - 4. Form InJllction and Clifford l s Theory We continue our examination of irreducible modules with a nonsingular form. 1) Hypothesis: group; and Assume that K is a finite field; G is a finite v is an irreducible V is a nonsingular classical bilinear form on V which is fixed by x V .. K G. In Section 1 part B(ii) we linked the induction structure of a symplectic module with the ten~or induction structure of a different irreducible mo- dule. The latter module was teusor primitive i f and only i f the symplectic module was fori.

Download PDF sample

3-Selmer groups for curves y^2 = x^3 + a by Bandini A.


by Mark
4.2

Bandini A.'s 3-Selmer groups for curves y^2 = x^3 + a PDF
Rated 4.31 of 5 – based on 25 votes