A closed Euler product formula for the genus set cardinality of Gorenstein cubic orders is derived via explicit local overorder classification.
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The algebraic stratification of Hitchin fibers via local smoothening types is proven equivalent to the geometric stratification by partial normalizations for GL_n in the Bass case, yielding an explicit cohomology formula for compactified Jacobians of spectral curves with double singularities.
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Ideal class monoids of cubic orders
A closed Euler product formula for the genus set cardinality of Gorenstein cubic orders is derived via explicit local overorder classification.
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Global geometrization of local smooth integral models in the Hitchin fibration for $\mathrm{GL}_n$: The Bass case
The algebraic stratification of Hitchin fibers via local smoothening types is proven equivalent to the geometric stratification by partial normalizations for GL_n in the Bass case, yielding an explicit cohomology formula for compactified Jacobians of spectral curves with double singularities.