By Lin Weg, Iku Nakamura

ISBN-10: 981256814X

ISBN-13: 9789812568144

Книга mathematics Geometry And quantity idea mathematics Geometry And quantity conception Книги Математика Автор: Lin Weg, Iku Nakamura Год издания: 2006 Формат: pdf Издат.:World clinical Publishing corporation Страниц: 412 Размер: thirteen ISBN: 981256814X Язык: Английский0 (голосов: zero) Оценка:Arithmetic Geometry And quantity conception (Number idea and Its Applications)By Lin Weg, Iku Nakamura

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**Extra info for Arithmetic Geometry And Number Theory**

**Example text**

M, so that we may regard Nj C M r for each j . ,m. Then one ob- Deligne Pairings over Moduli Spaces 41 tains a holomorphic family of Riemann surfaces {Mt>T} parametrized by the coordinates (t, r ) = ( i x , . . , r 3 3 _ 3 + A r _ m ) of A m x V ~ A m x A 3 s- 3 +^-" 1 . Moreover, the Riemann surfaces Mt,T with (t,r) € (A*) m x V are of type (g,N), where A* = A\{0}. , i m ) will be called pinching coordinates, and r = ( t i , . . , *3g-3+jv-m) will be called boundary coordinates. For 1 < j < m i let ay denote the simple closed curve |ZJ| = \WJ\ = \tj\2 on XtiT.

Invent. Math. 85 (1986), no. 1, 119145 K. -K. To k L. Weng 46 [W63] S. Wolpert, The hyperbolic metric and the geometry of universal curve. J. Differ. Gemo. 31 (1990) no. 2, 417-472 [Wo4] S. Wolpert, Cusps and the family hyperbolic metric, preprint, 2005 [X] G. Xiao, Fibered algebraic surfaces with low slope, Math. Ann. jp Vector Bundles on Curves over Cp Annette W E R N E R 1. Introduction This paper is a report on joint work with Christopher Deninger published in [De-Wel], [De-We2] and [De-We3].

K02] Kuo, W. Principal nilpotent orbits and reducible principal series. Represent. Theory 6 (2002), 127-159 (electronic). , On liftings and cusp cohomology of arithmetic groups. Invent. Math. 83(1986), no. 2, 383-401. [L89] Langlands, R. On the classification of irreducible representations of real algebraic groups. Representation Theory and Harmonic Analysis on Semisimple Lie Groups, Amer. Math. Soc, 1989, 101-170. [L04] Langlands, R. Beyond Endoscopy. Contributions to automorphic forms, geometry, and number theory, 611697, Johns Hopkins Univ.

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