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Milnor's conjecture for p-adic curves

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Speaker: 
Asher Auel
Affiliation: 
Penn St./Emory U/MPI
Date: 
Fri, 2011-01-28 11:15 - 12:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

The first cases of Milnor's conjecture on the fundamental filtration of the Witt ring of a field are settled by Kummer theory and by Merkurjev's theorem. Merkurjev's theorem---that every 2-torsion Brauer class is represented by the Clifford algebra of a quadratic form---is in general false when the base is no longer a field. Parimala, Scharlau, and Sridharan found smooth complete p-adic curves for which Merkurjev's theorem is equivalent to the existence of a rational theta characteristic. We'll discuss how replacing quadratic forms with their natural reductive counterparts, the so-called line bundle-valued quadratic forms, a generalized version of Milnor's conjecture for p-adic curves is obtained.

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