000			02130nam a22002655i 4500
001			18943149
003			ISI Library, Kolkata
005			20160427160618.0
008			160120s2016 nyu 000 0 eng
020			_a9783319273693 (hardcover : alk. paper)
040			_aISI Library _beng
082	0	4	_a516.35 _223 _bL973
100	1		_aLutkebohmert, Werner.
245	1	0	_aRigid geometry of curves and their jacobians / _cWerner Lutkebohmert.
260			_aCham : _bSpringer, _c2016.
300			_axviii, 386 p. : _billustrations ; _c24 cm.
490	0		_aErgebnisse der mathematik und ihrer grenzgebiete, 3. folge
490	0		_aA series of modern surveys in mathematics ; _v61.
504			_aIncludes bibliographical references and index.
505	0		_a1. Classical rigid geometry -- 2. Mumford curves -- 3. Formal and rigid geometry -- 4. Rigid analytic curves -- 5. Jacobian varieties -- 6. Raynaud extensions -- 7. Abeloid varieties -- Appendix -- Glossary of notations -- References -- Index.
520			_aThis book presents some of the most important aspects of rigid geometry, namely its applications to the study of smooth algebraic curves, of their Jacobians, and of abelian varieties - all of them defined over a complete non-archimedean valued field. The text starts with a survey of the foundation of rigid geometry, and then focuses on a detailed treatment of the applications. In the case of curves with split rational reduction there is a complete analogue to the fascinating theory of Riemann surfaces. In the case of proper smooth group varieties the uniformization and the construction of abelian varieties are treated in detail. Rigid geometry was established by John Tate and was enriched by a formal algebraic approach launched by Michel Raynaud. It has proved as a means to illustrate the geometric ideas behind the abstract methods of formal algebraic geometry as used by Mumford and Faltings. This book should be of great use to students wishing to enter this field, as well as those already working in it.
650		0	_aPlane curves.
650		0	_aJacobians.
942			_2ddc _cBK
999			_c420836 _d420836