On Hodge Structures and Periods -- Part I: Algebraic Aspects

TL;DR

This paper reviews Hodge structures, exploring their algebraic aspects, including filtrations, Galois theory, and Jordan-Holder structures, and compares periods of Riemann surfaces with algebraic number frameworks.

Contribution

It provides a comprehensive review connecting Hodge theory with Galois and algebraic structures, highlighting their interplay and differences.

Findings

Comparison of periods of Riemann surfaces with Galois-Artin algebraic numbers

Analysis of filtrations and Jordan-Holder structures in Hodge theory

Integration of Galois theory with Hodge structures

Abstract

We review Hodge structures, relating filtrations, Galois Theory and Jordan-Holder structures. The prototypical case of periods of Riemann surfaces is compared with the Galois-Artin framework of algebraic numbers.