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020 a| 9781470460211q| (paperback);

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100 1 a| Bilu, Margaret,d| 1990-?| UNAUTHORIZED;

245 10 a| Motivic Euler products and motivic height zeta functionsh| [electronic resource] /c| Margaret Bilu.;

260 a| Providence, RI :b| American Mathematical Society,c| 2023.;

300 a| v, 185 pages :b| illustrations ;c| 26 cm.;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| Volume 282, Number 1396;

504 a| Includes bibliographical references (pages 179-182) and index.;

505 0 a| Grothendieck rings of varieties and motivic vanishing cycles -- Motivic Euler products -- Mixed Hodge modules and convergence of Euler products -- The motivic Poisson formula -- Motivic height zeta functions.;

506 a| Available only to authorized users.;

520 a| "A motivic height zeta function associated to a family of varieties parametrised by a curve is the generating series of the classes, in the Grothendieck ring of varieties, of moduli spaces of sections of this family with varying degrees. This text is devoted to the study of the motivic height zeta function associated to a family of varieties with generic fiber having the structure of an equivariant compactification of a vector group. Our main theorem describes the convergence of this motivic height zeta function with respect to a topology on the Grothendieck ring of varieties coming from the theory of weights in cohomology. We deduce from it the asymptotic behaviour, as the degree goes to infinity, of a positive proportion of the coefficients of the Hodge-Deligne polynomial of the above moduli spaces: in particular, we get an estimate for their dimension and the number of components of maximal dimension. The main tools for this are a notion of motivic Euler product for series with coefficients in the Grothendieck ring of varieties, an extension of Hrushovski and Kazhdan's motivic Poisson summation formula, and a motivic measure on the Grothendieck ring of varieties with exponentials constructed using Denef and Loeser's motivic vanishing cycles"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Functions, Zeta.=| ^A55065;

650 0 a| Arithmetical algebraic geometry.=| ^A309723;

650 0 a| Geometry, Algebraic.=| ^A42380;

650 7 a| Algebraic geometry -- Birational geometry -- Arcs and motivic integration.2| msc;

650 7 a| Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Rational points.2| msc;

650 7 a| Number theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Heights.2| msc;

650 7 a| Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Arithmetic varieties and schemes; Arakelov theory; heights.2| msc;

655 0 a| Electronic books.=| ^A491897;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=30404207;

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Motivic Euler products and motivic height zeta functions / Margaret Bilu.

Author/creator	Bilu, Margaret, 1990-
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, 2023.
Description	v, 185 pages : illustrations ; 26 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Functions, Zeta. Arithmetical algebraic geometry. Geometry, Algebraic.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; Volume 282, Number 1396
Contents	Grothendieck rings of varieties and motivic vanishing cycles -- Motivic Euler products -- Mixed Hodge modules and convergence of Euler products -- The motivic Poisson formula -- Motivic height zeta functions.
Abstract	"A motivic height zeta function associated to a family of varieties parametrised by a curve is the generating series of the classes, in the Grothendieck ring of varieties, of moduli spaces of sections of this family with varying degrees. This text is devoted to the study of the motivic height zeta function associated to a family of varieties with generic fiber having the structure of an equivariant compactification of a vector group. Our main theorem describes the convergence of this motivic height zeta function with respect to a topology on the Grothendieck ring of varieties coming from the theory of weights in cohomology. We deduce from it the asymptotic behaviour, as the degree goes to infinity, of a positive proportion of the coefficients of the Hodge-Deligne polynomial of the above moduli spaces: in particular, we get an estimate for their dimension and the number of components of maximal dimension. The main tools for this are a notion of motivic Euler product for series with coefficients in the Grothendieck ring of varieties, an extension of Hrushovski and Kazhdan's motivic Poisson summation formula, and a motivic measure on the Grothendieck ring of varieties with exponentials constructed using Denef and Loeser's motivic vanishing cycles"-- Provided by publisher.
Bibliography note	Includes bibliographical references (pages 179-182) and index.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2023012959
ISBN	9781470460211 (paperback)
ISBN	(pdf)

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