On the Clemens-Schmid exact sequence
A treatment of (generalized) Clemens-Schmid exact sequences from the perspective of weights.
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arXiv subjects
R. Virk
Publications and source records attributed to R. Virk.
Realizations of exponential sheaves and Fourier transform
This note concerns exponential sheaves, their realizations, and Fourier transforms, in the setting of mixed Hodge modules and D-modules. For relative categories of exponential sheaves constructed out of regular/tame objects, we study realization functors to holonomic (not necessarily regular) D-modules and show that they are t-exact, faithful on the heart, and compatible with the usual functors (including Verdier duality). We also develop a "universal" Fourier transform: it is invertible, satisfies a Fourier miracle (commuting with Verdier duality up to a twist), and recovers classical Fourier transforms under realizations. The categories considered also admit weight structures that satisfy the standard formalism, and the "universal" Fourier transform preserves purity. The motivation is N. Katz's "analogies" between exponential sums over finite fields and differential equations.
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Hodge-Grothendieck classes and monodromy invariants of nearby cycles sheaves
Remarks on the Hodge-Grothendieck class of the nearby cycles functor and a generalized local invariant cycles result.
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Fourier-Sato transform for monodromic mixed Hodge modules
We discuss a construction of the Fourier-Sato transform for monodromic mixed Hodge modules.
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Homotopy limits and fixed point stacks
A discussion of homotopy limits of (1-)stacks, with an emphasis on fixed point stacks.
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Fixed points and Langlands parameter spaces for real groups
This note records that the Langlands parameter spaces, associated by Adams- Barbasch-Vogan to a real group, may be described as homotopy fixed points (fixed point stacks) of the spaces associated to the corresponding complex group.
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A remark on Ehresmann's Fibration Theorem
This note records that in the setting of complex varieties, the cohomological consequence of Ehresmann's fibration theorem holds without the smooth assumption on the base or the total space.
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Graded tensoring and crystals
An action of the $\mathfrak{sl}_2$-crystal category on graded/mixed (integral) category $\mathcal{O}$ `lifting' the usual tensor product is defined.
math.RT↗