Lech's conjecture

Lech's conjecture

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Linquan Ma , University of Utah
Fine Hall 322

A long-standing conjecture of Lech states that the Hilbert-Samuel multiplicity does not drop for faithfully flat extensions of local rings. This conjecture was known in dimension less than or equal to two and remains open in higher dimensions. In this talk we will use Hilbert-Kunz theory to obtain estimates on the multiplicities under faithfully flat extension, and in particular we can prove the conjecture in dimension three, in equal characteristic.