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Splitting and Making Explicit the de Rham Complex of the Drinfeld Space: 2397 (Lecture Notes in Mathematics, 2397) - Softcover

Breuil, Christophe; Qian, Zicheng

 
9783032200945: Splitting and Making Explicit the de Rham Complex of the Drinfeld Space: 2397 (Lecture Notes in Mathematics, 2397)
Softcover
ISBN 10: 3032200946 ISBN 13: 9783032200945
Verlag: Springer Nature Switzerland AG, 2026

Inhaltsangabe

This book gives a complete description of the de Rham complex of the Drinfeld space of dimension n - 1 as a complex of representations of GLn(K), where n ≥ 2 and K is a finite field extension of the field of p-adic numbers. The group GLn(K) acts on the Drinfeld space of dimension n - 1, hence on its complex of differential forms, yielding representations of GLn(K) that mathematicians began to study in the 1980s. Understanding these representations was one of the main motivations for the development of the theory of locally analytic representations of GLn(K), which can be seen as a p-adic analogue of Harish-Chandra’s (gln,K)-modules (in the latter, K is a maximal compact subgroup of GLn(R)). 

A transparent description is provided of the global sections of the de Rham complex of the Drinfeld space of dimension n-1 as a complex of (duals of) locally analytic representations of GLn(K), and an explicit partial splitting of this complex is constructed in the derived category of (duals of) locally analytic representations of GLn(K). Multiple intermediate results on Ext groups of locally analytic representations are established, which may be useful in other contexts. Requiring a light background in locally analytic representations, modules over enveloping algebras, and rigid spaces, the book is aimed at a general audience of number theorists and representation theorists.

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Über die Autorin bzw. den Autor

Christophe Breuil is the directeur de recherche CNRS at Université Paris-Saclay. His research interests include p-adic number theory, representation theory and algebraic geometry, with a focus on applications to the locally analytic, p-adic and mod p Langlands programs. He has published around 50 articles and preprints on this topic, including 4 books.

Zicheng Qian is an assistant professor (tenure track) at the Morningside Center of Mathematics of Beijing. His research interests includemod p and p-adic aspects of the Langlands program. He has published 6 articles and preprints on this topic, including 3 books.

Von der hinteren Coverseite

This book gives a complete description of the de Rham complex of the Drinfeld space of dimension n - 1 as a complex of representations of GLn(K), where n >= 2 and K is a finite field extension of the field of p-adic numbers. The group GLn(K) acts on the Drinfeld space of dimension n - 1, hence on its complex of differential forms, yielding representations of GLn(K) that mathematicians began to study in the 1980s. Understanding these representations was one of the main motivations for the development of the theory of locally analytic representations of GLn(K), which can be seen as a p-adic analogue of Harish-Chandra's (gln, K)-modules (in the latter, K is a maximal compact subgroup of GLn(R)).

A transparent description is provided of the global sections of the de Rham complex of the Drinfeld space of dimension n-1 as a complex of (duals of) locally analytic representations of GLn(K), and an explicit partial splitting of this complex is constructed in the derived category of (duals of) locally analytic representations of GLn(K). Multiple intermediate results on Ext groups of locally analytic representations are established, which may be useful in other contexts. Requiring a light background in locally analytic representations, modules over enveloping algebras, and rigid spaces, the book is aimed at a general audience of number theorists and representation theorists.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Springer Nature Switzerland AG
Erscheinungsdatum
2026
Sprache
Englisch
ISBN 10 
3032200946
ISBN 13 
9783032200945
Einband
Tapa blanda
Anzahl der Seiten
322
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