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001 978-3-642-23979-3
003 DE-He213
005 20160624101837.0
007 cr nn 008mamaa
008 120104s2012 gw | s |||| 0|eng d
020 _a9783642239793
_9978-3-642-23979-3
024 7 _a10.1007/978-3-642-23979-3
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
082 0 4 _a512.7
_223
100 1 _aHoward, Benjamin.
_eauthor.
245 1 0 _aIntersections of Hirzebruch–Zagier Divisors and CM Cycles
_h[electronic resource] /
_cby Benjamin Howard, Tonghai Yang.
260 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2012.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2012.
300 _aVIII, 140p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2041
505 0 _a1. Introduction -- 2. Linear Algebra -- 3. Moduli Spaces of Abelian Surfaces -- 4. Eisenstein Series -- 5. The Main Results -- 6. Local Calculations.
520 _aThis monograph treats one case of a series of conjectures by S. Kudla, whose goal is to show that Fourier of Eisenstein series encode information about the Arakelov intersection theory of special cycles on Shimura varieties of orthogonal and unitary type. Here, the Eisenstein series is a Hilbert modular form of weight one over a real quadratic field, the Shimura variety is a classical Hilbert modular surface, and the special cycles are complex multiplication points and the Hirzebruch–Zagier divisors. By developing new techniques in deformation theory, the authors successfully compute the Arakelov intersection multiplicities of these divisors, and show that they agree with the Fourier coefficients of derivatives of Eisenstein series.
650 0 _aMathematics.
650 0 _aNumber theory.
650 1 4 _aMathematics.
650 2 4 _aNumber Theory.
700 1 _aYang, Tonghai.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642239786
786 _dSpringer
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2041
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-23979-3
942 _2EBK1984
_cEBK
999 _c31278
_d31278