Number Theory, Analysis and Geometry by Dorian Goldfeld Jay Jorgenson Peter Jones Dinakar Ramakrishnan Kenneth Ribet & John Tate

Author:Dorian Goldfeld, Jay Jorgenson, Peter Jones, Dinakar Ramakrishnan, Kenneth Ribet & John Tate
Language: eng
Format: epub
Publisher: Springer US, Boston, MA

If d = 2n is even, we first look to see whether or not there are infinitely many good primes ℓ where our orthogonal group is nonsplit. If there are, we choose r large enough that

and we take any list of r good primes

at which the corresponding orthogonal group is nonsplit.

If d = 2n is even, and there are at most finitely many good primes ℓ where our orthogonal group is nonsplit, then we choose r large enough that

and we take any list of r good primes

at which the corresponding orthogonal group is split.

We now study what happens in the geometric generic fibre of M ∕ R. Denote by K the fraction field of R, by an algebraic closure of K, and by the -scheme obtained by the extension of scalars .

Denote by

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