Étale motives of geometric origin - Revision history

Cid36224 at 06:53, 3 June 2024

2024-06-03T06:53:12Z

← Older revision		Revision as of 08:53, 3 June 2024
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	Raphaël Ruimy - Étale motives of geometric origin.		Raphaël Ruimy - '''Étale motives of geometric origin'''.

	In "Étale motives", Cisinski and Déglise defined two finiteness conditions on étale motives: motives that come from geometry and motives that are dualisable over a stratification. In a joint paper with S. Tubach, we showed that both conditions give the same category. To prove this, we first reduce to the case of fields by use the six functors and continuity, then we use some results on Artin motives and a result of Balmer and Gallauer on representations of finite groups. We also prove that geometric étale motives satisfy Milnor excision. I will then explain some applications to Nori motives with integral coefficients and arc-descent for them.		In "Étale motives", Cisinski and Déglise defined two finiteness conditions on étale motives: motives that come from geometry and motives that are dualisable over a stratification. In a joint paper with S. Tubach, we showed that both conditions give the same category. To prove this, we first reduce to the case of fields by use the six functors and continuity, then we use some results on Artin motives and a result of Balmer and Gallauer on representations of finite groups. We also prove that geometric étale motives satisfy Milnor excision. I will then explain some applications to Nori motives with integral coefficients and arc-descent for them.

Cid36224 at 06:52, 3 June 2024

2024-06-03T06:52:54Z

← Older revision		Revision as of 08:52, 3 June 2024
Line 1:		Line 1:
	In "Étale motives", Cisinski and Déglise defined two finiteness conditions on étale motives: motives that come from geometry and motives that are dualisable over a stratification.		Raphaël Ruimy - Étale motives of geometric origin.
	In a joint paper with S. Tubach, we showed that both conditions give the same category. To prove this, we first reduce to the case of fields by use the six functors and continuity, then we use some results on Artin motives and a result of Balmer and Gallauer on representations of finite groups. We also prove that geometric étale motives satisfy Milnor excision.
	I will then explain some applications to Nori motives with integral coefficients and arc-descent for them.		In "Étale motives", Cisinski and Déglise defined two finiteness conditions on étale motives: motives that come from geometry and motives that are dualisable over a stratification. In a joint paper with S. Tubach, we showed that both conditions give the same category. To prove this, we first reduce to the case of fields by use the six functors and continuity, then we use some results on Artin motives and a result of Balmer and Gallauer on representations of finite groups. We also prove that geometric étale motives satisfy Milnor excision. I will then explain some applications to Nori motives with integral coefficients and arc-descent for them.

Cid36224: Created page with " In "Étale motives", Cisinski and Déglise defined two finiteness conditions on étale motives: motives that come from geometry and motives that are dualisable over a st..."

2024-06-03T06:51:13Z

Created page with " In "Étale motives", Cisinski and Déglise defined two finiteness conditions on étale motives: motives that come from geometry and motives that are dualisable over a st..."

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In "Étale motives", Cisinski and Déglise defined two finiteness conditions on étale motives: motives that come from geometry and motives that are dualisable over a stratification.
In a joint paper with S. Tubach, we showed that both conditions give the same category. To prove this, we first reduce to the case of fields by use the six functors and continuity, then we use some results on Artin motives and a result of Balmer and Gallauer on representations of finite groups. We also prove that geometric étale motives satisfy Milnor excision.
I will then explain some applications to Nori motives with integral coefficients and arc-descent for them.