---
title: "Motivic Integration" 
---

# Motivic Integration

## Meta

- CiteKey: "CNS18"
- Type: book
- Author: "Chambert-Loir, Antoine; Nicaise, Johannes; Sebag, Julien;"  
- Publisher: "Springer New York,"
- Year: 2018 
- Collections: "Syllabus; Talbot 2022; Talbot 2022,"
- **Original URL**: <http://link.springer.com/10.1007/978-1-4939-7887-8>
- Open local files directly: [Chambert-Loir et al. - 2018 - Motivic Integration.pdf](file:///home/zack/Zotero/storage/YDX9U9ND/Chambert-Loir%20et%20al.%20-%202018%20-%20Motivic%20Integration.pdf#page=71)
- **Open in Zotero**: [Zotero](zotero://select/library/items/CWLWQD4L)

## Abstract

## Notes

- Computing the classes of $\AA^n$ and $\PP^n$, as well as algebraic vector bundles: see [Section 2.4](zotero://open-pdf/library/items/YDX9U9ND?page=90):
	![](attachments/Pasted%20image%2020220609185743.png)
	![](attachments/Pasted%20image%2020220609185822.png)

----

## Extracted Annotations


Annotations(6/9/2022, 4:00:12 PM)

![[CNS18_TYTBMEQJ.png]] [(Chambert-Loir et al., 2018, p. IX)](zotero://open-pdf/library/items/YDX9U9ND?page=9&annotation=GLPNJ84U)

![[CNS18_ARUDI8G8.png]] [(Chambert-Loir et al., 2018, p. X)](zotero://open-pdf/library/items/YDX9U9ND?page=10&annotation=TZDILTNH)

![[CNS18_7TCVVBVD.png]] [(Chambert-Loir et al., 2018, p. X)](zotero://open-pdf/library/items/YDX9U9ND?page=10&annotation=9CFM7ARH)

![[CNS18_I3CS6LHC.png]] [(Chambert-Loir et al., 2018, p. X)](zotero://open-pdf/library/items/YDX9U9ND?page=10&annotation=ICN28HWZ)

![[CNS18_Y782SCSX.png]] [(Chambert-Loir et al., 2018, p. XI)](zotero://open-pdf/library/items/YDX9U9ND?page=11&annotation=E9UFUBW4)

![[CNS18_3BBWK56F.png]] [(Chambert-Loir et al., 2018, p. XI)](zotero://open-pdf/library/items/YDX9U9ND?page=11&annotation=S9WH4SZH)

![[CNS18_F2RZL3QE.png]] [(Chambert-Loir et al., 2018, p. XI)](zotero://open-pdf/library/items/YDX9U9ND?page=11&annotation=UDNBE52J)

![[CNS18_2FBAWAYF.png]] [(Chambert-Loir et al., 2018, p. XI)](zotero://open-pdf/library/items/YDX9U9ND?page=11&annotation=383I8SC6)

![[CNS18_HZVGE2RS.png]] [(Chambert-Loir et al., 2018, p. XII)](zotero://open-pdf/library/items/YDX9U9ND?page=12&annotation=RQB5WY7H)

![[CNS18_BDKHGH2V.png]] [(Chambert-Loir et al., 2018, p. XII)](zotero://open-pdf/library/items/YDX9U9ND?page=12&annotation=ERYYG3AW)

![[CNS18_82YYFWAC.png]] [(Chambert-Loir et al., 2018, p. 465)](zotero://open-pdf/library/items/YDX9U9ND?page=481&annotation=CM86NCJK)

![[CNS18_44A2NQNR.png]] [(Chambert-Loir et al., 2018, p. 465)](zotero://open-pdf/library/items/YDX9U9ND?page=481&annotation=PRBWRCZV)

![[CNS18_D4RNXT83.png]] [(Chambert-Loir et al., 2018, p. 467)](zotero://open-pdf/library/items/YDX9U9ND?page=483&annotation=LMWSA9PM)

![[CNS18_VTBJZDBP.png]] [(Chambert-Loir et al., 2018, p. 468)](zotero://open-pdf/library/items/YDX9U9ND?page=484&annotation=RJQ3BQFM)

-  Appendix on [[birational geometry]].

![[CNS18_9KM97I4R.png]] [(Chambert-Loir et al., 2018, p. 469)](zotero://open-pdf/library/items/YDX9U9ND?page=485&annotation=LRJLUSDF)

![[CNS18_NK75TS5B.png]] [(Chambert-Loir et al., 2018, p. 469)](zotero://open-pdf/library/items/YDX9U9ND?page=485&annotation=XBWBPQ8Y)

![[CNS18_WSAZHSYD.png]] [(Chambert-Loir et al., 2018, p. 469)](zotero://open-pdf/library/items/YDX9U9ND?page=485&annotation=D5FUPF2A)

![[CNS18_2HNACGAI.png]] [(Chambert-Loir et al., 2018, p. 469)](zotero://open-pdf/library/items/YDX9U9ND?page=485&annotation=9KE3DS3B)

![[CNS18_E35C3JAA.png]] [(Chambert-Loir et al., 2018, p. 470)](zotero://open-pdf/library/items/YDX9U9ND?page=486&annotation=PIC33XRW)

![[CNS18_QRAPXN6Q.png]] [(Chambert-Loir et al., 2018, p. 470)](zotero://open-pdf/library/items/YDX9U9ND?page=486&annotation=KF832648)

![[CNS18_5BE4PBSL.png]] [(Chambert-Loir et al., 2018, p. 470)](zotero://open-pdf/library/items/YDX9U9ND?page=486&annotation=2DZX5KVI)

![[CNS18_YET42INU.png]] [(Chambert-Loir et al., 2018, p. 470)](zotero://open-pdf/library/items/YDX9U9ND?page=486&annotation=R3SQUHLH)

![[CNS18_SU7U8LGR.png]] [(Chambert-Loir et al., 2018, p. 470)](zotero://open-pdf/library/items/YDX9U9ND?page=486&annotation=GQZ4W8RF)

![[CNS18_SKB5PJWU.png]] [(Chambert-Loir et al., 2018, p. 470)](zotero://open-pdf/library/items/YDX9U9ND?page=486&annotation=JY5IPP4J)

![[CNS18_TM7LAYS9.png]] [(Chambert-Loir et al., 2018, p. 471)](zotero://open-pdf/library/items/YDX9U9ND?page=487&annotation=KUBGC4SK)

![[CNS18_NN4Q7YEM.png]] [(Chambert-Loir et al., 2018, p. 471)](zotero://open-pdf/library/items/YDX9U9ND?page=487&annotation=BS8KA3JJ)

-  blowdown

![[CNS18_TNSZ64FF.png]] [(Chambert-Loir et al., 2018, p. 471)](zotero://open-pdf/library/items/YDX9U9ND?page=487&annotation=8SZ9GUI4)

-  [[weak factorization]] theorem

![[CNS18_L2PMYEU6.png]] [(Chambert-Loir et al., 2018, p. 471)](zotero://open-pdf/library/items/YDX9U9ND?page=487&annotation=ZU4YEVSR)

-  [[weak factorization]] theorem, relation to [[strong factorization]] conjecture

![[CNS18_D5G6SWP4.png]] [(Chambert-Loir et al., 2018, p. 472)](zotero://open-pdf/library/items/YDX9U9ND?page=488&annotation=6IPRRPAF)

![[CNS18_G9P8YIJH.png]] [(Chambert-Loir et al., 2018, p. 472)](zotero://open-pdf/library/items/YDX9U9ND?page=488&annotation=CC8HHDSA)

![[CNS18_HCZX3CKG.png]] [(Chambert-Loir et al., 2018, p. 473)](zotero://open-pdf/library/items/YDX9U9ND?page=489&annotation=S8MX9F5Y)

![[CNS18_Z4T98FL9.png]] [(Chambert-Loir et al., 2018, p. 473)](zotero://open-pdf/library/items/YDX9U9ND?page=489&annotation=8F6CQRPR)

![[CNS18_IS239KZK.png]] [(Chambert-Loir et al., 2018, p. 473)](zotero://open-pdf/library/items/YDX9U9ND?page=489&annotation=3S2C7AQY)

![[CNS18_CSJ45IC7.png]] [(Chambert-Loir et al., 2018, p. 474)](zotero://open-pdf/library/items/YDX9U9ND?page=490&annotation=MZINJ627)

![[CNS18_SXHBZW6C.png]] [(Chambert-Loir et al., 2018, p. 474)](zotero://open-pdf/library/items/YDX9U9ND?page=490&annotation=QSVMFAQJ)

![[CNS18_YA6BGAV7.png]] [(Chambert-Loir et al., 2018, p. 474)](zotero://open-pdf/library/items/YDX9U9ND?page=490&annotation=4GPGE3RG)

![[CNS18_ZBNJJCH9.png]] [(Chambert-Loir et al., 2018, p. 474)](zotero://open-pdf/library/items/YDX9U9ND?page=490&annotation=8PX7863M)

![[CNS18_U38DP5CG.png]] [(Chambert-Loir et al., 2018, p. 475)](zotero://open-pdf/library/items/YDX9U9ND?page=491&annotation=LNIE52EE)

![[CNS18_FMLEZ3DP.png]] [(Chambert-Loir et al., 2018, p. 475)](zotero://open-pdf/library/items/YDX9U9ND?page=491&annotation=CKR4B4N6)

![[CNS18_NVMLDMSN.png]] [(Chambert-Loir et al., 2018, p. 475)](zotero://open-pdf/library/items/YDX9U9ND?page=491&annotation=FYCES8A6)

![[CNS18_FUY6DCVX.png]] [(Chambert-Loir et al., 2018, p. 476)](zotero://open-pdf/library/items/YDX9U9ND?page=492&annotation=H9CFEL8L)

![[CNS18_RZ628BEP.png]] [(Chambert-Loir et al., 2018, p. 476)](zotero://open-pdf/library/items/YDX9U9ND?page=492&annotation=IJQFQELJ)

![[CNS18_IF2RVF5V.png]] [(Chambert-Loir et al., 2018, p. 476)](zotero://open-pdf/library/items/YDX9U9ND?page=492&annotation=SWNT728Z)

![[CNS18_LM7IAWQK.png]] [(Chambert-Loir et al., 2018, p. 476)](zotero://open-pdf/library/items/YDX9U9ND?page=492&annotation=ZZLU6I37)

![[CNS18_WZ854BVQ.png]] [(Chambert-Loir et al., 2018, p. 476)](zotero://open-pdf/library/items/YDX9U9ND?page=492&annotation=78KCM57E)

![[CNS18_PTTHXCNK.png]] [(Chambert-Loir et al., 2018, p. 477)](zotero://open-pdf/library/items/YDX9U9ND?page=493&annotation=VS5NSDCZ)

![[CNS18_VRNWVSXW.png]] [(Chambert-Loir et al., 2018, p. 477)](zotero://open-pdf/library/items/YDX9U9ND?page=493&annotation=GC58MU5K)

-  Appendix on [[formal geometry]]

![[CNS18_M2JZ8J5R.png]] [(Chambert-Loir et al., 2018, p. 478)](zotero://open-pdf/library/items/YDX9U9ND?page=494&annotation=BRGBXKFI)

![[CNS18_G2EVZ69H.png]] [(Chambert-Loir et al., 2018, p. 478)](zotero://open-pdf/library/items/YDX9U9ND?page=494&annotation=KRN25XZN)

![[CNS18_HD98JIVT.png]] [(Chambert-Loir et al., 2018, p. 478)](zotero://open-pdf/library/items/YDX9U9ND?page=494&annotation=VQR5C3QX)

![[CNS18_BI8KSN6D.png]] [(Chambert-Loir et al., 2018, p. 478)](zotero://open-pdf/library/items/YDX9U9ND?page=494&annotation=FICHJ52G)

![[CNS18_TCUP2KRT.png]] [(Chambert-Loir et al., 2018, p. 479)](zotero://open-pdf/library/items/YDX9U9ND?page=495&annotation=UUMYCTXY)

![[CNS18_V7Q7NPW5.png]] [(Chambert-Loir et al., 2018, p. 479)](zotero://open-pdf/library/items/YDX9U9ND?page=495&annotation=IACSEJUD)

![[CNS18_LTIVDYFX.png]] [(Chambert-Loir et al., 2018, p. 479)](zotero://open-pdf/library/items/YDX9U9ND?page=495&annotation=QVKIFM94)

![[CNS18_H6PHVUZ2.png]] [(Chambert-Loir et al., 2018, p. 479)](zotero://open-pdf/library/items/YDX9U9ND?page=495&annotation=JQNNRYK9)

![[CNS18_WDP6Y3AM.png]] [(Chambert-Loir et al., 2018, p. 479)](zotero://open-pdf/library/items/YDX9U9ND?page=495&annotation=79J8JEL9)

![[CNS18_2C8N84UA.png]] [(Chambert-Loir et al., 2018, p. 480)](zotero://open-pdf/library/items/YDX9U9ND?page=496&annotation=ZIU8PRI3)

![[CNS18_45DCHR8V.png]] [(Chambert-Loir et al., 2018, p. 480)](zotero://open-pdf/library/items/YDX9U9ND?page=496&annotation=QY8EF5NQ)

![[CNS18_2CUVMYC4.png]] [(Chambert-Loir et al., 2018, p. 480)](zotero://open-pdf/library/items/YDX9U9ND?page=496&annotation=5FTQNJ25)

![[CNS18_AY2ZXTWD.png]] [(Chambert-Loir et al., 2018, p. 480)](zotero://open-pdf/library/items/YDX9U9ND?page=496&annotation=3ZYSKLXN)

![[CNS18_RWNKN86R.png]] [(Chambert-Loir et al., 2018, p. 481)](zotero://open-pdf/library/items/YDX9U9ND?page=497&annotation=MHU93TZ3)

![[CNS18_VII32QR5.png]] [(Chambert-Loir et al., 2018, p. 481)](zotero://open-pdf/library/items/YDX9U9ND?page=497&annotation=7SSLSS32)

![[CNS18_VRCD4KLK.png]] [(Chambert-Loir et al., 2018, p. 481)](zotero://open-pdf/library/items/YDX9U9ND?page=497&annotation=656BIGNP)

![[CNS18_KPVTFFJX.png]] [(Chambert-Loir et al., 2018, p. 481)](zotero://open-pdf/library/items/YDX9U9ND?page=497&annotation=9XRM22PN)

![[CNS18_72FXU5RU.png]] [(Chambert-Loir et al., 2018, p. 481)](zotero://open-pdf/library/items/YDX9U9ND?page=497&annotation=7ED9KNQU)

![[CNS18_UJC9MUEP.png]] [(Chambert-Loir et al., 2018, p. 482)](zotero://open-pdf/library/items/YDX9U9ND?page=498&annotation=STDS3SDU)

![[CNS18_S8D97IA3.png]] [(Chambert-Loir et al., 2018, p. 482)](zotero://open-pdf/library/items/YDX9U9ND?page=498&annotation=M6GUVGBQ)

-  algebra of [[convergent power series]]

![[CNS18_TTU7TL8K.png]] [(Chambert-Loir et al., 2018, p. 483)](zotero://open-pdf/library/items/YDX9U9ND?page=499&annotation=8T3WXK93)

![[CNS18_I6579KXK.png]] [(Chambert-Loir et al., 2018, p. 484)](zotero://open-pdf/library/items/YDX9U9ND?page=500&annotation=GAMND93P)

![[CNS18_L6GNT7CX.png]] [(Chambert-Loir et al., 2018, p. 484)](zotero://open-pdf/library/items/YDX9U9ND?page=500&annotation=VW5G5K57)

![[CNS18_KVNIAH76.png]] [(Chambert-Loir et al., 2018, p. 484)](zotero://open-pdf/library/items/YDX9U9ND?page=500&annotation=UV3NP2NT)

![[CNS18_7755FWYN.png]] [(Chambert-Loir et al., 2018, p. 486)](zotero://open-pdf/library/items/YDX9U9ND?page=502&annotation=442ELV2B)

![[CNS18_Y7M7QBUR.png]] [(Chambert-Loir et al., 2018, p. 486)](zotero://open-pdf/library/items/YDX9U9ND?page=502&annotation=UP59WZWC)

![[CNS18_ZAV543FA.png]] [(Chambert-Loir et al., 2018, p. 486)](zotero://open-pdf/library/items/YDX9U9ND?page=502&annotation=T27HXGC5)

![[CNS18_6IYXH4L3.png]] [(Chambert-Loir et al., 2018, p. 487)](zotero://open-pdf/library/items/YDX9U9ND?page=503&annotation=Y48AP7NT)

![[CNS18_LL54GVSU.png]] [(Chambert-Loir et al., 2018, p. 487)](zotero://open-pdf/library/items/YDX9U9ND?page=503&annotation=Q8WI6JZ6)

![[CNS18_JT9Q3GEK.png]] [(Chambert-Loir et al., 2018, p. 487)](zotero://open-pdf/library/items/YDX9U9ND?page=503&annotation=3FIR8FK7)

![[CNS18_YR3I87SY.png]] [(Chambert-Loir et al., 2018, p. 488)](zotero://open-pdf/library/items/YDX9U9ND?page=504&annotation=DF6RKH5M)

![[CNS18_5SB4C56T.png]] [(Chambert-Loir et al., 2018, p. 488)](zotero://open-pdf/library/items/YDX9U9ND?page=504&annotation=DYP7XH8J)

![[CNS18_GPZTVGCP.png]] [(Chambert-Loir et al., 2018, p. 488)](zotero://open-pdf/library/items/YDX9U9ND?page=504&annotation=IBJDY2L6)

![[CNS18_BLCHPGYG.png]] [(Chambert-Loir et al., 2018, p. 489)](zotero://open-pdf/library/items/YDX9U9ND?page=505&annotation=8CYDRA5L)

![[CNS18_RA7CF9SQ.png]] [(Chambert-Loir et al., 2018, p. 489)](zotero://open-pdf/library/items/YDX9U9ND?page=505&annotation=F6T2INMW)

![[CNS18_CAR86ANF.png]] [(Chambert-Loir et al., 2018, p. 489)](zotero://open-pdf/library/items/YDX9U9ND?page=505&annotation=FGJEA4K8)

![[CNS18_GX8K333L.png]] [(Chambert-Loir et al., 2018, p. 489)](zotero://open-pdf/library/items/YDX9U9ND?page=505&annotation=AGTUM5DA)

![[CNS18_AK2CGM9Q.png]] [(Chambert-Loir et al., 2018, p. 490)](zotero://open-pdf/library/items/YDX9U9ND?page=506&annotation=LP9Y6JJX)

![[CNS18_97M2TVR6.png]] [(Chambert-Loir et al., 2018, p. 491)](zotero://open-pdf/library/items/YDX9U9ND?page=507&annotation=5BFW8EE6)

![[CNS18_32FR75D8.png]] [(Chambert-Loir et al., 2018, p. 492)](zotero://open-pdf/library/items/YDX9U9ND?page=508&annotation=NHP2LF89)

![[CNS18_EJ7PFYAQ.png]] [(Chambert-Loir et al., 2018, p. 492)](zotero://open-pdf/library/items/YDX9U9ND?page=508&annotation=PK55DY4I)

![[CNS18_3I6DTXAV.png]] [(Chambert-Loir et al., 2018, p. 496)](zotero://open-pdf/library/items/YDX9U9ND?page=512&annotation=HYAAGEMD)

![[CNS18_QFKMZAXR.png]] [(Chambert-Loir et al., 2018, p. 497)](zotero://open-pdf/library/items/YDX9U9ND?page=513&annotation=MTIM5BJ5)