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We carry out the log minimal model program for the moduli space
of stable hyperelliptic curves and show that certain log canonical models of
are isomorphic to the proper transform of
in the corresponding log canonical models of
We define Hecke operators for vector valued modular forms transforming with the Weil representation associated to a discriminant form. We describe the properties of the corresponding algebra of Hecke operators and study the action on modular forms.
Let A be an Azumaya algebra of constant rank n
2 over a Hensel pair (R, I) where R is a semilocal ring with n invertible in R. Then the reduced Whitehead group SK1(A) coincides with its reduction SK1(A/I A). This generalizes a result of Hazrat (J Algebra 305:687–703, 2006) to non-local Henselian...
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