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Représentations $$p$$-adiques de Groupes $$p$$-adiques III: Méthodes Globales et Géométriques
 Astérisque 2010; 469 pp; softcover Number: 331 ISBN-10: 2-85629-282-8 ISBN-13: 978-2-85629-282-2 List Price: US$90 Member Price: US$72 Order Code: AST/331 In this last volume on the local $$p$$-adic correspondence for $$\mathrm{GL}_2(\mathbf Q_p)$$, the editors have gathered papers which, mostly, do not use directly the $$(\phi,\Gamma)$$-module theory. The methods and results are often geometric ($$p$$-adic comparison theorems, de Rham cohomology of the Drinfeld half-plane), or global (local-global compatibility with étale completed cohomology). There are also papers on $$p$$-adic Hodge theory and the $$\mathcal L$$-invariant and important local results on extensions between certain representations of $$\mathrm{GL}_2(\mathbf Q_p)$$. A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicians interested in number theory. Table of Contents G. Stevens -- Goleman's $$\mathcal{L}$$-invariant and families of modular forms P. Colmez -- Invariants $$\mathcal{L}$$ et dérivées de valeurs propres de Frobenius M. Bertolini, H. Darmon, and A. Iovita -- Families of automorphic forms on definite quaternion algebras and Teitelbaum's conjecture C. Breuil -- Série spéciale $$p$$-adique et cohomologie étale complétée C. Breuil and A. Mézard -- Représentations semi-stables de $$\mathrm{GL}_2(\mathbb{Q}_p)$$, demi-plan $$p$$-adique et réduction modulo $$p$$ R. Coleman and A. Iovita -- Hidden structures on semistable curves C. Breuil and M. Emerton -- Représentations $$p$$-adiques ordinaires de $$\mathbf{GL}_2(\mathbf{Q}_p)$$ et compatibilité local-global V. Paškūnas -- Extensions for supersingular representations of $$\mathrm{GL}_2(\mathbb{Q}_p)$$ M. Emerton -- Ordinary parts of admissible representations of $$p$$-adic reductive groups I. Definition and first properties M. Emerton -- Ordinary parts of admissible representations of $$p$$-adic reductive groups II. Derived functors M. Emerton and V. Paškūnas -- On the effaceability of certain $$\delta$$-functors