Paper XIStatements and proofs
Statements and proofs
Find a statement anywhere in this work by title, printed number, type or source label. Entries follow the chapter order. Each proof link opens the written proof passage.
Statements by chapter
Weil Deligne chains
Tame Frobenius packets
- Proposition 3.1: Tame character projectors Read proof
- Theorem 3.2: Tame orbit induction Read proof
- Corollary 3.3: Dimension and regularity Read proof
- Proposition 3.4: Dual and self dual tame packets Read proof
- Proposition 3.5: Unramified twist Read proof
- Proposition 3.6: Möbius orbit count Read proof
- Example 3.7: Degree four over ( FF 2 )
Finite field cuspidal projectors
Tensor refinement of tame atoms
- Theorem 5.1: Greatest common divisor and least common multiple packets Read proof
- Corollary 5.2: Packet count and dimension Read proof
- Proposition 5.3: Refined exponent formula Read proof
- Proposition 5.4: Local polynomial of one tame packet Read proof
- Corollary 5.5: Tame tensor local factor Read proof
- Proposition 5.6: Trivial tensor packet criterion Read proof
- Corollary 5.7: Tame Hom test Read proof
- Proposition 5.8: Conductor of a nontrivial tame atom Read proof
Finite Gauss phases
Finite Heisenberg packets
Twisted group algebras and commutator envelopes
A restricted one break Galois envelope
- Definition 9.1: One break Clifford datum
- Proposition 9.2: Clifford multiplicity action Read proof
- Definition 9.3: Clifford cocycle class
- Proposition 9.4: Intrinsic commutator pairing Read proof
- Definition 9.5: One break symplectic envelope
- Theorem 9.6: Nondegenerate one break packet Read proof
- Proposition 9.7: Isomorphism invariance Read proof
- Proposition 9.8: Tame stabilizer action Read proof
- Corollary 9.9: Heisenberg representation attached to one break Read proof
- Remark 9.10
The type side symplectic quotient
The restricted Galois to type bridge
- Definition 11.1: Bridge datum
- Theorem 11.2: Restricted Heisenberg bridge Read proof
- Proposition 11.3: Cyclic discrepancy character Read proof
- Lemma 11.4: Linearization over a cyclic stabilizer Read proof
- Theorem 11.5: One phase closes the cyclic bridge Read proof
- Corollary 11.6: Bridge uniqueness Read proof
- Remark 11.7
Odd residue characteristic phases
- Standard fact 12.1: Fixed point free Weil trace
- Definition 12.2: Odd finite Weil phase
- Proposition 12.3: Symplectic invariance Read proof
- Proposition 12.4: Orthogonal multiplicativity Read proof
- Corollary 12.5: Characteristic polynomial certificate Read proof
- Proposition 12.6: Fixed and moving decomposition Read proof
- Definition 12.7: Moving phase
- Proposition 12.8: Hyperbolic phase formula Read proof
- Corollary 12.9: Phase only bridge test Read proof
- Remark 12.10
Dyadic quadratic refinements
- Definition 13.1: Quadratic refinement
- Proposition 13.2: Affine space of refinements Read proof
- Definition 13.3: Arf invariant
- Standard fact 13.4: Arf invariance and classification
- Theorem 13.5: Dyadic Gauss sign Read proof
- Corollary 13.6: Orthogonal dyadic multiplicativity Read proof
- Proposition 13.7: The form alone does not determine the phase Read proof
- Proposition 13.8: Translation of quadratic refinements Read proof
- Theorem 13.9: Number of dyadic refinements Read proof
Matrix holonomy and finite gluing
- Definition 14.1: Path transport
- Theorem 14.2: Matrix holonomy criterion Read proof
- Corollary 14.3: Unbased gauge classification Read proof
- Corollary 14.4: Scalar and projective gluing Read proof
- Proposition 14.5: Projective cocycle form Read proof
- Proposition 14.6: Exact edge residual from cycle defect Read proof
- Corollary 14.7: Quantitative finite gluing Read proof
- Remark 14.8