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Lecture

Monodromy Conjecture

In course

MATH-494: Topics in arithmetic geometry

P-adic numbers are a number theoretic analogue of the real numbers, which interpolate between arithmetics, analysis and geometry. In this course we study their basic properties and give various applications, notably we will prove rationality of the Weil Ze ...

Description

This lecture covers the Monodromy Conjecture, discussing the origins and implications of this mathematical statement for archimedean local fields. Starting with the analogue statement for archimedean local fields, the instructor explains the smooth continuation and eigenvalues of some Mx. The lecture progresses to define the Bernstein-polynomial and its significance in the context of the conjecture, illustrating the simple proof and the conditions for convergence. The session concludes by exploring the expected truth of the conjecture and its implications for different scenarios.

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