Microlocal composition and pure sheaves

Two lessons explain how kernel germs compose at prescribed covectors and how closed half-space tests define pure and simple sheaves with their exact shifts. Fourteen exercises have complete solutions.

The proofs use the stated ordinary kernel calculus, localized-category cutoff and direct-image theorems, conormal coefficient models, contact normal forms and ordered Lagrangian index identities. Coefficients are arbitrary bounded modules over a commutative ring of finite global dimension. Simplicity and nonvanishing examples assume a nonzero ring.

The exact preceding proof providers are not included in this download; their revision bindings and transitive source checks remain open. The source comparison in each lesson identifies what its freely readable references prove. It does not replace the stated programme inputs or certify completion of the parent course.

Download the readings, editable sources and build code · Reuse terms · Provenance