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LEADER 03395cam 2200493 i 4500

003 OCoLC;

005 20141212062102.0;

008 130228t20132013riua b 001 0 eng ;

010 a| 2012048281;

020 a| 9780821894347;

020 a| 082189434X (alk. paper);

035 a| (Sirsi) 99956037321;

035 a| 99956037321;

035 a| (OCoLC)823209442;

042 a| pcc;

050 4 a| QA1b| .U558 v.61;

050 00 a| QA564b| .M873 2013;

082 00 a| 516.3/52| 23;

084 a| 14C15a| 14C25a| 13D152| msc;

100 1 a| Murre, Jacob P.,d| 1929-=| ^A73374;

245 10 a| Lectures on the theory of pure motives /c| Jacob P. Murre, Jan Nagel, Chris A. M. Peters.;

264 1 a| Providence, Rhode Island :b| American Mathematical Society,c| [2013];

300 a| ix, 149 pages ;c| 25 cm.;

336 a| text2| rdacontent;

337 a| unmediated2| rdamedia;

338 a| volume2| rdacarrier;

490 1 a| University lecture series ;v| volume 61;

504 a| Includes bibliographical references (pages 139-144) and indexes.;

505 0 a| 1. Algebraic cycles and equivalence relations -- 2. Motives: construction and first properties -- 3. On Grothendieck's standard conjectures -- 4. Finite dimensionality of motives -- 5. Properties of finite dimensional motives -- 6. Chow-Künneth decomposition in a special case -- 7. On the conjectural Bloch-Beilinson filtration -- 8. Relative Chow-Künneth decomposition -- 9. Beyond pure motives.;

520 3 a| The theory of motives was created by Grothendieck in the 1960s as he searched for a universal cohomology theory for algebraic varieties. The theory of pure motives is well established as far as the construction is concerned. Pure motives are expected to have a number of additional properties predicted by Grothendieck's standard conjectures, but these conjectures remain wide open. The theory for mixed motives is still incomplete. This book deals primarily with the theory of pure motives. The exposition begins with the fundamentals: Grothendieck's construction of the category of pure motives and examples. Next, the standard conjectures and the famous theorem of Jannsen on the category of the numerical motives are discussed. Following this, the important theory of finite dimensionality is covered. The concept of Chow-Künneth decomposition is introduced, with discussion of the known results and the related conjectures, in particular the conjectures of Bloch-Beilinson type. We finish with a chapter on relative motives and a chapter giving a short introduction to Voevodsky's theory of mixed motives -- P. 4 of cover.;

650 0 a| Motives (Mathematics)=| ^A368273;

650 7 a| Algebraic geometry -- Cycles and subschemes -- (Equivariant) Chow groups and rings; motives.2| msc;

650 7 a| Algebraic geometry -- Cycles and subschemes -- Algebraic cycles.2| msc;

650 7 a| Commutative algebra -- Homological methods -- Grothendieck groups, $K$-theory.2| msc;

700 1 a| Nagel, Jan.=| ^A718173;

700 1 a| Peters, C.q| (Chris)=| ^A565108;

830 0 a| University lecture series (Providence, R.I.) ;v| v. 61.=| ^A344893;

960 o| 1s| 44.00t| Joyner48u| JMATz| USD;

982 a| 99956037321;

596 a| 1;

998 a| 3397103;

999 a| QA564 .M873 2013w| LCc| 1i| 30372016147669l| JGESm| JOYNERr| Ys| Yt| JGESBKu| 3/12/2014x| BOOKz| JSTACKS;

Lectures on the theory of pure motives / Jacob P. Murre, Jan Nagel, Chris A. M. Peters.

Author/creator	Murre, Jacob P., 1929-
Other author	Nagel, Jan.
Other author	Peters, C. (Chris)
Format	Book
Publication	Providence, Rhode Island : American Mathematical Society, [2013]
Copyright Date	©2013
Description	ix, 149 pages ; 25 cm.
Subjects	Motives (Mathematics)

Series	University lecture series ; volume 61 University lecture series (Providence, R.I.) ; v. 61. ^A344893
Contents	1. Algebraic cycles and equivalence relations -- 2. Motives: construction and first properties -- 3. On Grothendieck's standard conjectures -- 4. Finite dimensionality of motives -- 5. Properties of finite dimensional motives -- 6. Chow-Künneth decomposition in a special case -- 7. On the conjectural Bloch-Beilinson filtration -- 8. Relative Chow-Künneth decomposition -- 9. Beyond pure motives.
Summary	The theory of motives was created by Grothendieck in the 1960s as he searched for a universal cohomology theory for algebraic varieties. The theory of pure motives is well established as far as the construction is concerned. Pure motives are expected to have a number of additional properties predicted by Grothendieck's standard conjectures, but these conjectures remain wide open. The theory for mixed motives is still incomplete. This book deals primarily with the theory of pure motives. The exposition begins with the fundamentals: Grothendieck's construction of the category of pure motives and examples. Next, the standard conjectures and the famous theorem of Jannsen on the category of the numerical motives are discussed. Following this, the important theory of finite dimensionality is covered. The concept of Chow-Künneth decomposition is introduced, with discussion of the known results and the related conjectures, in particular the conjectures of Bloch-Beilinson type. We finish with a chapter on relative motives and a chapter giving a short introduction to Voevodsky's theory of mixed motives -- P. 4 of cover.
Bibliography note	Includes bibliographical references (pages 139-144) and indexes.
LCCN	2012048281
ISBN	9780821894347
ISBN	082189434X (alk. paper)

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Lectures on the theory of pure motives / Jacob P. Murre, Jan Nagel, Chris A. M. Peters.

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