When: Oct. 07 2019, 14:30.
Where: Gauss

Speaker : Junyeong Park (Postech)

Title : A homotopy Lie formula for the $p$-adic Dwork Frobenius operator

Abstract : Given a smooth projective complete intersection $X$ over a finite field, there is the notion of zeta function defined as a generation function. Dwork's theory recovers the zeta function as a characteristic polynomial of his Frobenius operator''. In this talk, we will give an interpretation of this via deformation theory of homotopy Lie algebra. Using this we will explicitly construct a Differential Gerstenhaber-Batalin-Vilkovisky (DGBV) algebra for $X$, motivated by the corresponding situation in complex geometry. As a consequence, we get a formula for the $p$-adic Dwork operator in terms of a morphism of homotopy Lie algebras.