On Mochizuki's idea of Anabelomorphy and its applications

Abstract

Ordinarity of a local Galois representation is amphoric 17 Φ Sen is unamphoric 19 Artin and Swan Conductor of a local Galois representation are not amphoric 20 Peu and Tres ramifiedness are not amphoric properties 21 Discriminant and Different of a p-adic field are unamphoric 22 Frobenius elements are amphoric 24 Monoradicality is amphoric 24 Anabelomorphy for Tate curves and Abelian varieties with multiplicative reduction 25 Anabelomorphy of group-schemes of type (p, p, • • • , p) over p-adic fields 27 Anabelomorphy for Projective Spaces and Affine spaces 27 The L-invariant is unamphoric 29 Anabelomorphic Connectivity Theorem for Number Fields 30 The Ordinary Synchronization Theorem 37 Automorphic Synchronization Theorems: Anabelomorphy and the local Langlands correspondence 40 Anabelomorphic Density Theorem 44 Anabelomorphic Connectivity Theorem for Elliptic Curves 45 Anabelomorphy and Fundamental Groups 47 Anabelomorphy of Elliptic Curves II: Kodaira Symbol, Exponent of Conductor and Tamagawa Number are all unamphoric 49 Artin Conductors, Swan Conductors and Discriminants II 24 The theory of Tate curves at archimedean primes and Θ-functions at archimedean primes 54 25 Anabelomorphic Density Theorem II 58 26 Perfectoid algebraic geometry as an example of anabelomorphy 61 27 The proof of the Fontaine-Colmez Theorem as an example of anabelomorphy on the Hodge side 62 28 Anabelomorphy for p-adic differential equations 64