منابع مشابه
Galois Descent
Let L/K be a field extension. A K-vector space W can be extended to an L-vector space L⊗KW , and W embeds into L⊗KW by w 7→ 1⊗w. Under this embedding, when W 6= 0 a K-basis {ei} of W turns into an L-basis {1⊗ ei} of L⊗KW . Passing from W to L⊗KW is called ascent. In the other direction, if we are given an L-vector space V 6= 0, we may ask how to describe the K-subspaces W ⊂ V such that a K-basi...
متن کاملGalois invariants of dessins d’enfants
The two main problems of the theory of dessins d’enfants are the following: i) given a dessin, i.e., a purely combinatorial object, find the equations for β and X explicitly; ii) find a list of (combinatorial? topological? algebraic?) invariants of dessins which completely identify their Gal(Q̄/Q)-orbits. The second problem can be interestingly weakened from Gal(Q̄/Q) to ĜT , but it remains absol...
متن کاملIwasawa invariants of galois deformations
of the absolute Galois group of a number field F . Assume that ρ̄ is ordinary in the sense that the image of any decomposition group at a place v dividing p lies in some Borel subgroup Bv of G. Assume also that ρ̄ satisfies the conditions of [11, Section 7] which guarantee that it has a reasonable deformation theory; see Section 3.1 for details. In this paper we show that the Iwasawa invariants o...
متن کاملTwo Step Descent in Modular Galois
We propound a Descent Principle by which previously constructed equations over GF(q n)(X) may be deformed to have incarnations over GF(q)(X) without changing their Galois groups, where q = p u > 1 is a power of a prime p and n is a positive integer. Currently this is achieved by starting with a vectorial (= additive) q-polynomial of q-degree m with Galois group GL(m; q) where m is any positive ...
متن کاملGalois Descent and Severi-brauer Varieties
We say an algebraic object or property over a field k is arithmetic if it becomes trivial or vanishes after finite separable base extension. Since such objects or properties owe their existence to the presence of “arithmetic gaps” in k, i.e., the failure of k to be algebraically closed, we view them as responses to specific arithmetic properties of k, and we study them in order to gain insight ...
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2014
ISSN: 0024-6093
DOI: 10.1112/blms/bdt108