On congruent isomorphisms for tori
Anne-Marie Aubert, Sandeep Varma

TL;DR
This paper constructs and analyzes congruent isomorphisms between tori over close nonarchimedean local fields, demonstrating their functoriality, compatibility with known homomorphisms, and respect for the local Langlands correspondence.
Contribution
It introduces a new congruent isomorphism for tori over close fields, extending previous work and ensuring compatibility with key structures like the Kottwitz homomorphism and local Langlands correspondence.
Findings
Constructed congruent isomorphisms between tori over close fields.
Proved functoriality and compatibility with existing homomorphisms.
Showed the isomorphisms respect the local Langlands correspondence.
Abstract
Let and be two -close nonarchimedean local fields, where is a positive integer, and let and be two tori over and , respectively, such that their cocharacter lattices can be identified as modules over the ''at most -ramified'' absolute Galois group . In the spirit of the work of Kazhdan and Ganapathy, for every positive integer relative to which is large, we construct a congruent isomorphism , where and are the minimal congruent filtration subgroups of and , respectively, defined by J.-K.~Yu. We prove that this isomorphism is functorial and compatible with both the isomorphism constructed by Chai and Yu and the Kottwitz homomorphism for tori. We show…
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models
