Descent of affine buildings - I. Large minimal angles

TL;DR

This paper proves the existence of affine buildings from exceptional algebraic groups with large minimal angles, completing a conjecture by Jacques Tits and laying foundational work for the theory.

Contribution

It establishes the existence of affine buildings for exceptional groups with large minimal angles, advancing the understanding of their geometric structures.

Findings

Proves existence of affine buildings for exceptional algebraic groups

Completes the conjecture by Jacques Tits for these groups

Lays foundational framework for further research

Abstract

In this two-part paper we prove an existence result for affine buildings arising from exceptional algebraic reductive groups. Combined with earlier results on classical groups, this gives a complete and positive answer to the conjecture concerning the existence of affine buildings arising from such groups defined over a (skew) field with a complete valuation, as proposed by Jacques Tits. This first part lays the foundations for our approach and deals with the `large minimal angle' case.