Séminaire Arithmétique et géométrie algébrique
organisé par l'équipe Arithmétique et géométrie algébrique
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Lin Zhou
On the infinite generation of morphic and motivic cohomology
22 janvier 2026 - 14:00Salle de séminaires IRMA
Since Mumford’s work in the 1960s, questions on the finite generation of Chow and Griffiths groups—such as the finiteness of dimension, the size of their torsion, or their divisibility—have been a central theme in the study of algebraic cycles. Motivic cohomology and morphic cohomology naturally generalize the Chow group (cycles modulo rational equivalence) and cycles modulo algebraic equivalence. In this talk, I will show how, over an algebraically closed field whose transcendence degree over its prime field is infinite (e.g., the complex number field), one can combine Schoen’s injectivity argument with Schreieder’s refined unramified cohomology to construct examples of motivic and morphic cohomology groups with infinitely many torsion elements. These appear to be the first known examples exhibiting infinite torsion in motivic or morphic cohomology. Joint work with Theodosis Alexandrou.