100, rue des maths 38610 Gières / GPS : 45.193055, 5.772076 / Directeur : Louis Funar

Daniel Schaeppi

Hermite rings and symplectic K-theory
Lundi, 19 Février, 2024 - 14:00
Résumé : 
A finitely generated projective module is stably free if it becomes free after taking the direct sum with a finitely generated free module. A commutative ring R is called a Hermite ring if all stably free R-modules are free. Examples include rings where all finitely generated projective modules are free (such as polynomial rings over a field), and all Dedekind domains.
 In his book on Serre's problem, Lam asked if the following conjecture is true: if R is a Hermite ring, then the polynomial ring in one variable R[x] is also Hermite. This conjecture is known as the Hermite ring conjecture.
 In my talk I will explain how certain computations in symplectic K-theory can be used to construct a counterexample to the Hermite ring conjecture.


Institution de l'orateur : 
Universität Regensburg
Thème de recherche : 
Algèbre et géométries
Salle : 
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