Sheaf proof readings

Constructibility, sheaf operations and microlocal geometry. Each reading includes its exact editable source.

Constructibility prerequisites

• Constructibility from microsupport and perfect stalks · source
• Perfect coefficients on compact fibres · source
• Perfect operations and finite microlocal coefficients · source
• Conic subanalytic images and isotropic dimension · source
• Isotropic cotangent transport and discrete critical values · source
• Limiting cotangent sums and characteristic inverse images · source
• When a kernel quantizes a contact transformation · source
• Constructible costalks and Verdier duality · source
• Complex microlocal stratifications and constructibility · source
• Holomorphic operations and complex Fourier symmetries · source
• Constructible sheaves on a triangulation · source

Further proof readings

• Normal scaling, microlocal Hom and involutivity · source

• Microlocal stratifications by removing bad loci · source

• Unshared conormal directions and dimension filtrations · source

• Involutive subsets of subanalytic isotropic sets · source

• Weak constructibility under sheaf operations · source

• Constructible gluing on an interval · source

• Derived constructibility through common triangulations · source

• Subanalytic sets and limiting tangent directions · source

• Boundary forms and Lagrangian normal cones · source

• Dual kernels and an unchanged parameter · source

• Directional morphisms through a sheaf kernel · source

• SH02-LFI — Local models and change of ambient manifold · source

• Local morphisms in cotangent directions · source

• Small balls, central fibres and supported cohomology · source

• Directional neighborhoods and the compact-cap test · source

• Limiting covectors at open boundaries · source

• Analytic normal cones through complex deformation · source

• Analytic conormal covers and singular involutivity · source

• Finite conormal closures and generic base directions · source

• Directional tests at a constructible boundary · source

• Perverse support, costalks and truncation triangles · source

• Complex-constructible sheaves and missing derived classes · source

• Kernels that preserve chosen cotangent directions · source

• Adjoints of localized sheaf kernels · source

• SH02-MHPC — Transporting both inputs before forming internal Hom · source

• SH02-MEP-UNIT. Following the comparison maps into the normal bundle · source

• SH02-MHPR — Product recovery for microlocal composition · source

• SH02-EXCEPTIONAL-OPERATIONS — Exceptional inverse image from a finite resolution · source

• SH02-MD — Local orientations, dimension, and integration · source

• SH02-CB-UNIT — Finite local data and sheaf biduality · source

• SH02-GAM — Directional neighborhoods and a sheaf projector · source

• Moving Fourier kernels across maps and products · source

• Reading a sheaf at the normal scale · source

• Covector tests of normal limits · source

• Composing sheaf operators through an intermediate space · source

• Complex conicity and analytic Lagrangian closures · source

• SH02-MST — Detecting and removing directional obstructions · source

• Sheaf kernels and cotangent correspondences · source

• Truncation triangles and abelian hearts · source

• Perverse descent and fibre dimension bounds · source

• Complex middle perversity and exterior products · source

• SH02-MC — Categories and operations in one cotangent direction · source

• SH02-FTE-UNIT. Transposing the complete Fourier trace comparison · source

• SH02-PREREQ-OPEN — Open prerequisites and exact import contracts · source

• SH02-CA — Extending sections on convex sets · source

• Transport along a scaling action · source

• SH02-FSB — Formal stabilization over arbitrary neighborhood sets · source

• Fourier kernels as radial averaging · source

• SH02-FGC-UNIT. The graded line in a Fourier support comparison · source

• SH02-NCD — Continuing cohomology through a moving boundary · source

• SH02-MO-UNIT — Transporting directional obstructions · source

• T-exact functors and adjoints between hearts · source

• SH02-LFT. A linear map inside the Fourier comparison · source

• SH02-NDF-UNIT. The geometric normalization of Fourier adjunctions · source

• SH02-PREREQ-PROOFS — Supporting verifications for open prerequisites · source

• SH02-UR — Finite resolutions without a lower bound · source

• SH02-SUP-EXH-001 — Recovering sheaf cohomology from closed pieces · source

• Fourier duality through a test complex on the base · source

• SH02-SUB-UNIT — Reading a subset through its sheaf · source

• SH02-FTC. Comparing traces after Fourier transformation · source

• SH02-CHE-UNIT — Cotangent directions that survive a limiting operation · source

• SH02-UCE — Uniform tests for an unbounded Hom complex · source

• SH02-SIX-BRIDGE — Proper supports and the bounded classical comparison · source

• SH02-NG-UNIT — Normal geometry as a family with a central fibre · source

• SH02-AE-UNIT — Covectors at a boundary and at infinity · source

Learner route: from a diagram to a heart

Begin with constructible gluing on an interval, then constructible sheaves on a triangulation, followed by perverse support and truncation triangles.

Edition and source records · Source notices