The $b$-pseudodifferential calculus on Galois coverings and a higher Atiyah-Patodi-Singer index theorem

Mémoires de la Société mathématique de France ◽

10.24033/msmf.382 ◽

1997 ◽

Vol 1 ◽

pp. 1-123

Author(s):

Éric Leichtnam ◽

Paolo Piazza

Keyword(s):

Index Theorem ◽

Pseudodifferential Calculus ◽

Galois Coverings

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The relative L2 index theorem for Galois coverings

Annals of K-Theory ◽

10.2140/akt.2021.6.503 ◽

2021 ◽

Vol 6 (3) ◽

pp. 503-541

Author(s):

Moulay-Tahar Benameur

Keyword(s):

Index Theorem ◽

Galois Coverings ◽

L2 Index

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A note on the higher Atiyah–Patodi–Singer index theorem on Galois coverings

Journal of Noncommutative Geometry ◽

10.4171/jncg/234 ◽

2016 ◽

Vol 10 (1) ◽

pp. 261-302 ◽

Cited By ~ 2

Author(s):

Alexander Gorokhovsky ◽

Hitoshi Moriyoshi ◽

Paolo Piazza

Keyword(s):

Index Theorem ◽

Galois Coverings

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Preliminaries

10.23943/princeton/9780691161686.003.0002 ◽

2017 ◽

Author(s):

Ehud Hrushovski ◽

François Loeser

Keyword(s):

Valued Fields ◽

Definable Set ◽

Valued Field ◽

Galois Coverings ◽

Definable Type ◽

Definable Sets ◽

Background Material

This chapter provides some background material on definable sets, definable types, orthogonality to a definable set, and stable domination, especially in the valued field context. It considers more specifically these concepts in the framework of the theory ACVF of algebraically closed valued fields and describes the definable types concentrating on a stable definable V as an ind-definable set. It also proves a key result that demonstrates definable types as integrals of stably dominated types along some definable type on the value group sort. Finally, it discusses the notion of pseudo-Galois coverings. Every nonempty definable set over an algebraically closed substructure of a model of ACVF extends to a definable type.

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