The Langlands Program, Motives, and l-independence

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• Suvir Rathore, University of Cambridge
• Friday 14 November 2025, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Xuanchun Lu.

Grothendieck’s philosophy of motives suggests the l-adic etale cohomology of a variety should be independent of the prime number l in some sense. Deligne’s proof of the Weil conjectures and in particular the (geometric) Riemann hypothesis sheds light on a numerical statement of l-independence which led Deligne to make a more general conjecture. A geometric refinement of l-independence was given by Serre using Frobenius tori and later Drinfeld using Deligne’s conjecture (known for smooth varieties) and a known instance of the Langlands conjectures due to (Laurent) Lafforgue.

We will give a brief introduction to motives as a universal cohomology theory in algebraic geometry and the Langland’s program in number theory, with application to l-independence.

This talk is part of the Junior Geometry Seminar series.

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