galois representation造句

• His research interest is in modular forms and Galois representations.
• Galois representations are in fact isogenous, and hence have the same conductor.
• He introduced the concept of geometric Galois representation of the Galois group of a number field.
• This then has application to the theory of Galois representations, and particularly semistable Galois representations.
• This then has application to the theory of Galois representations, and particularly semistable Galois representations.
• There are also Galois representations that arise from auxiliary objects and can be used to study Galois groups.
• In the theory of Shimura varieties it associates automorphic representations of other groups to certain-adic Galois representations as well.
• The question of which extensions can be found is that of the Tate modules of such varieties, as Galois representations.
• Caraiani graduated summa cum laude from Princeton in 2007, with an undergraduate thesis on Galois representations supervised by Andrew Wiles.
• Galois representation of a rational newform cannot be isomorphic to that of an irrational newform of level " N ".
• This showed that a proof of the Serre's conjecture on modular Galois representations, which would imply the modularity theorem.
• He won the 2005 Fermat Prize for his contributions to the study of L-functions and p-adic Galois representations.
• The proof of Fermat's Last Theorem proceeds by first reinterpreting elliptic curves and modular forms in terms of these Galois representations.
• All this is part of the " yoga of weights ", uniting Hodge theory and the l-adic Galois representations.
• Another formulation depends on the comparison of Galois representations attached on the one hand to elliptic curves, and on the other hand to modular forms.
• Group schemes that are not algebraic groups play a significant role in arithmetic geometry and algebraic topology, since they come up in contexts of Galois representations and moduli problems.
• The original context for the formulation of the group in question was the question of the Galois representation on the Tate module of an abelian variety " A ".
• Galois actions on the group schemes transfer through the equivalences of categories, and the associated deformation theory of Galois representations was used in Wiles's work on the Shimura Taniyama conjecture.
• He is interested in " arithmetic over number fields and its interaction with geometry over the complex numbers . " Much of his early work was on modular forms and the associated Galois representations.
• This difference gives formal groups a rich geometric theory in positive and mixed characteristic, with connections to the Steenrod algebra, " p "-divisible groups, Dieudonn?theory, and Galois representations.