Geodesic
On the behavior of stringy motives under Galois quasi-étale covers
Javier Carvajal-Rojas1 orcid ; Takehiko Yasuda2 orcid
1Centro de Investigación en Matemáticas, A.C., Guanajuato, Mexico
2Osaka University, Osaka, Japan
Documenta mathematica, Tome 30 (2025) no. 3, pp. 709-751

Voir la notice de l'article provenant de la source EMS Press

We investigate the behavior of stringy motives under Galois quasi-étale covers. We prove that they descend under such covers in a sense defined via their Poincaré realizations. Further, we show that such descent is strict in the presence of ramification. As a corollary, we reduce the problem regarding the finiteness of the étale fundamental group of KLT singularities to a DCC property for their stringy motives. We verify such DCC property for surfaces in arbitrary characteristic. As an application, we give a characteristic-free proof for the finiteness of the étale fundamental group of log terminal surface singularities, which was unknown in equal characteristics 2 and 3 and in mixed characteristics.
DOI : 10.4171/dm/1012
Classification : 14B05, 14E18, 14E30, 14E20
Mots-clés : Kawamata log-terminal, stringy motive, étale fundamental group

Javier Carvajal-Rojas  1   ; Takehiko Yasuda  2

1 Centro de Investigación en Matemáticas, A.C., Guanajuato, Mexico
2 Osaka University, Osaka, Japan 
Javier Carvajal-Rojas; Takehiko Yasuda. On the behavior of stringy motives under Galois quasi-étale covers. Documenta mathematica, Tome 30 (2025) no. 3, pp. 709-751. doi: 10.4171/dm/1012
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