REVIEW 2 cited by
A choice-free absolute Galois group and Artin motives
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
Proofs that an arbitrary field has a separable closure are necessarily non-constructive, and separable closures are unique only up to non-canonical isomorphism. This means that the absolute Galois group of a field is defined only up to inner automorphism. Here we construct a profinite algebraic group which is an inner form of the absolute Galois group. Our construction uses no form of the axiom of choice, and the group is defined up to canonical isomorphism. We also show that the Frobenius associated with a prime of a number field unramified in an extension, which is classically defined only up to conjugation, has a uniquely-defined analogue in terms of our group. We give a construction of the category of Artin motives with coefficients in an arbitrary field, and we give an interpretation of our absolute Galois group in terms of this category.
Forward citations
Cited by 2 Pith papers
-
On the finite transcendence of Frobenius traces for abelian varieties over $\mathbb{Q}$
Establishes transcendence of Frobenius traces for non-CM elliptic curves over Q and for several abelian varieties over Q.
-
Positive characteristic analogues of finite algebraic numbers
A positive-characteristic analogue of Rosen's finite algebraic numbers is introduced over F_q(θ) and is characterized by linear recurrent sequences with separable eigen polynomial, Frobenius evaluation, and matrix coe...
Discussion (0). Continue with ORCID to comment.