Generalizations and minimalistic refinements of the t-birational Section Conjecture

TL;DR

This paper extends the t-birational Section Conjecture to more base fields and introduces minimalistic Galois-theoretic refinements, advancing understanding of the conjecture's scope.

Contribution

It generalizes the t-BSC to broader base fields and provides minimalistic refinements involving less Galois information.

Findings

Extended the class of base fields where t-BSC holds

Proved minimalistic Galois-theoretic refinements of t-BSC

Enhanced understanding of the conjecture's applicability

Abstract

In this note we give generalizations and prove 'minimalistic' refinements of the t-birational Section Conjecture (t-BSC), cf. [Be], by doing both: First, by extending the class of base fields over which the t-BSC holds, and second, by proving refinements of the t-BSC which involve much less, that is minimalistic, Galois theoretical information.