This talk focuses on the algebraic viewpoint of ordinary linear differential equations $Ly=0$ with rational function coefficients. The main question is when such a differential equation has a full basis of algebraic solutions. The Grothendieck-Katz conjecture tries to answer this question: It states that $Ly=0$ has such a basis if and only if the $p$-curvature is zero for almost all primes $p$.
The talk will motivate this conjecture and provide a proof for the case of order one equations $y' + r(x)y = 0$, with $r$ a rational function in one variable $x$.
A gentle introduction to the Grothendieck-Katz conjecture
27.11.2025 09:30 - 10:45
Organiser:
H. Hauser
Location: