Algebraic tori as Nisnevich sheaves with transfers
Annales de la faculté des sciences de Toulouse Mathématiques (2014)
- Volume: 23, Issue: 3, page 699-715
- ISSN: 0240-2963
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topKahn, Bruno. "Algebraic tori as Nisnevich sheaves with transfers." Annales de la faculté des sciences de Toulouse Mathématiques 23.3 (2014): 699-715. <http://eudml.org/doc/275402>.
@article{Kahn2014,
abstract = {We relate $R$-equivalence on tori with Voevodsky’s theory of homotopy invariant Nisnevich sheaves with transfers and effective motivic complexes.},
author = {Kahn, Bruno},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {-equivalence; -torus; Nisnevich sheaves; motivic complexes},
language = {eng},
number = {3},
pages = {699-715},
publisher = {Université Paul Sabatier, Toulouse},
title = {Algebraic tori as Nisnevich sheaves with transfers},
url = {http://eudml.org/doc/275402},
volume = {23},
year = {2014},
}
TY - JOUR
AU - Kahn, Bruno
TI - Algebraic tori as Nisnevich sheaves with transfers
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2014
PB - Université Paul Sabatier, Toulouse
VL - 23
IS - 3
SP - 699
EP - 715
AB - We relate $R$-equivalence on tori with Voevodsky’s theory of homotopy invariant Nisnevich sheaves with transfers and effective motivic complexes.
LA - eng
KW - -equivalence; -torus; Nisnevich sheaves; motivic complexes
UR - http://eudml.org/doc/275402
ER -
References
top- Barbieri-Viale (L.), Kahn (B.).— On the derived category of -motives, arXiv:1009.1900.
- Borovoi (M.), Kunyavskǐi (B. E‘), Lemire (N.), Reichstein (Z.).— Stably Cayley groups in characteristic zero, IMRN (2013).
- Colliot-Thélène (J.-L.), Harari (D.), Skorobogatov (A.).— Compactification équivariante d’un tore (d’après Brylinski et Künnemann), Expo. Math. 23, p. 161-170 (2005). Zbl1078.14076MR2155008
- Colliot-Thélène (J.-L.), Sansuc (J.-J.).— La -équivalence sur les tores, Ann. Sci. Éc. Norm. Sup. 10, p. 175-230 (1977). Zbl0356.14007MR450280
- Colliot-Thélène (J.-L.), Sansuc (J.-J.).— Principal homogeneous spaces under flasque tori; applications, J. Alg. 106, p. 148-205 (1987). Zbl0597.14014MR878473
- Gille (P.).— La -équivalence pour les groupes algébriques réductifs définis sur un corps global, Publ. Math. IHÉS 86, p. 199-235 (1997). Zbl0943.20044MR1608570
- Gille (P.).— Spécialisation de la -équivalence pour les groupes réductifs, Trans. Amer. Math. Soc. 356, p. 4465-4474 (2004). Zbl1067.20063MR2067129
- Huber (A.) and Kahn (B.).— The slice filtration and mixed Tate motives, Compositio Math. 142, p. 907-936 (2006). Zbl1105.14022MR2249535
- Kahn (B.).— Sur le groupe des classes d’un schéma arithmétique (avec un appendice de Marc Hindry), Bull. Soc. Math. France 134 (2006), p. 395-415. Zbl1222.14048MR2245999
- Kahn (B.), Yamazaki (T.).— Voevodsky’s motives and Weil reciprocity, Duke Math. J. 162, p. 2751-2796 (2013). Zbl1309.19009MR3127813
- Kahn (B.), Sujatha (R.).— Birational motives, I (preliminary version), preprint, 2002, http://www.math.uiuc.edu/K-theory/0596/.
- Merkurjev (A. S.).— -equivalence on three-dimensional tori and zero-cycles, Algebra Number Theory 2, p. 69-89 (2008). Zbl1210.19005MR2377363
- Merkurjev (A. S.).— Zero-cycles on algebraic tori, in The geometry of algebraic cycles, 119-122, Clay Math. Proc., 9, Amer. Math. Soc., Providence, RI (2010). Zbl1221.14008MR2648668
- Morel (F.), Voevodsky (V.).— -homotopy theory of schemes, Publ. Math. IHÉS 90, p. 45-143 (1999). Zbl0983.14007MR1813224
- Mumford (D.).— Abelian varieties (corrected reprint), TIFR - Hindustan Book Agency (2008). Zbl1177.14001MR2514037
- Serre J.-P..— Morphismes universels et variétés d’Albanese, in Exposés de séminaires, 1950-1989, Doc. mathématiques 1, SMF, p. 141-160 (2001). Zbl0123.13903MR160229
- Spiess (M.), T. Szamuely (T.).— On the Albanese map for smooth quasi-projective varieties, Math. Ann. 325, p. 1-17 (2003). Zbl1077.14026MR1957261
- Voevodsky (V.).— Cohomological theory of presheaves with transfers, in E. Friedlander, A. Suslin, Voevodsky (V.) Cycles, transfers and motivic cohomology theories, Ann. Math. Studies 143, Princeton University Press, 88-137 (2000). Zbl1019.14010MR1764200
- Voevodsky (V.).— Triangulated categories of motives over a field, in E. Friedlander, A. Suslin, Voevodsky (V.) Cycles, transfers and motivic cohomology theories, Ann. Math. Studies 143, Princeton University Press, p. 188-238 (2000). Zbl1019.14009MR1764202
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