Seattle lectures on motivic integration

2009 ◽  
pp. 745-784 ◽  
Author(s):  
François Loeser
Keyword(s):  
Motivic Integration

Motivic Integration in Josquin's "Motets"

1977 ◽  
Vol 21 (2) ◽  
pp. 264 ◽  
Author(s):  
Irving Godt ◽  
Josquin
Keyword(s):  
Motivic Integration

Motivic Integration

2018 ◽  
Author(s):  
Antoine Chambert-Loir ◽  
Johannes Nicaise ◽  
Julien Sebag
Keyword(s):  
Motivic Integration

scholarly journals Tropical refined curve counting via motivic integration

2018 ◽  
Vol 22 (6) ◽  
pp. 3175-3234 ◽  
Author(s):  
Johannes Nicaise ◽  
Sam Payne ◽  
Franziska Schroeter
Keyword(s):  
Motivic Integration

scholarly journals POINCARÉ SERIES FOR SEVERAL PLANE DIVISORIAL VALUATIONS

2003 ◽  
Vol 46 (2) ◽  
pp. 501-509 ◽  
Author(s):  
F. Delgado ◽  
S. M. Gusein-Zade
Keyword(s):  
Plane Curve ◽  
Poincaré Series ◽  
Finite Collection ◽  
Curve Singularity ◽  
Motivic Integration ◽  
Poincare Series ◽  
Plane Curve Singularity ◽  
Functions Of Two Variables ◽  
Irreducible Components ◽  
Divisorial Valuations

AbstractWe compute the (generalized) Poincaré series of the multi-index filtration defined by a finite collection of divisorial valuations on the ring $\mathcal{O}_{\mathbb{C}^2,0}$ of germs of functions of two variables. We use the method initially elaborated by the authors and Campillo for computing the similar Poincaré series for the valuations defined by the irreducible components of a plane curve singularity. The method is essentially based on the notions of the so-called extended semigroup and of the integral with respect to the Euler characteristic over the projectivization of the space of germs of functions of two variables. The last notion is similar to (and inspired by) the notion of the motivic integration.AMS 2000 Mathematics subject classification: Primary 14B05; 16W70

scholarly journals The motivic Thom–Sebastiani theorem for regular and formal functions

2018 ◽  
Vol 2018 (735) ◽  
pp. 175-198 ◽  
Author(s):  
Quy Thuong Lê
Keyword(s):  
Analogous Result ◽  
Motivic Integration ◽  
Crucial Element ◽  
Regular Functions ◽  
Formal Schemes ◽  
Theoretic Proof

AbstractThanks to the work of Hrushovski and Loeser on motivic Milnor fibers, we give a model-theoretic proof for the motivic Thom–Sebastiani theorem in the case of regular functions. Moreover, slightly extending Hrushovski–Loeser’s construction adjusted to Sebag, Loeser and Nicaise’s motivic integration for formal schemes and rigid varieties, we formulate and prove an analogous result for formal functions. The latter is meaningful as it has been a crucial element of constructing Kontsevich–Soibelman’s theory of motivic Donaldson–Thomas invariants.

scholarly journals Motivic Haar Measure on Reductive Groups

2006 ◽  
Vol 58 (1) ◽  
pp. 93-114
Author(s):  
Julia Gordon
Keyword(s):  
Haar Measure ◽  
Explicit Construction ◽  
Closed Field ◽  
Motivic Integration ◽  
Reductive Groups ◽  
Base Field ◽  
Locally Compact ◽  
Grothendieck Ring ◽  
Reductive Algebraic Group ◽  
Made In

AbstractWe define a motivic analogue of the Haar measure for groups of the form G(k((t))), where k is an algebraically closed field of characteristic zero, and G is a reductive algebraic group defined over k. A classical Haar measure on such groups does not exist since they are not locally compact. We use the theory of motivic integration introduced by M. Kontsevich to define an additive function on a certain natural Boolean algebra of subsets of G(k((t))). This function takes values in the so-called dimensional completion of the Grothendieck ring of the category of varieties over the base field. It is invariant under translations by all elements of G(k((t))), and therefore we call it a motivic analogue of Haar measure. We give an explicit construction of the motivic Haar measure, and then prove that the result is independent of all the choices that are made in the process.

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