12 papers
Homological stability and weak approximation
Sho Tanimoto, Yuri Tschinkel
We investigate homological stability for the space of sections of Fano fibrations over curves in the context of weak approximation, and establish it for projective bundles, as well…
Geometric Manin's conjecture in characteristic
Brian Lehmann, Sho Tanimoto
Geometric Manin's conjecture for complex Fano varieties describes the structure of the moduli space of curves. We propose a version of this conjecture in characteristic and des…
Manin's conjecture for semi-integral curves and -connectedness
Qile Chen, Brian Lehmann, Sho Tanimoto
We explore log Manin's conjecture for integral points and its connections to -connectedness. We prove log Manin's conjecture for Campana rational curves and for $\math…
Homological sieve and Manin's conjecture
Sho Tanimoto
This is a report of the author's talk at RIMS workshop Algebraic Number Theory and Related Topics 2025 which was held at RIMS Kyoto University during December 15th-19th 2025. In th…
The spaces of rational curves on del Pezzo surfaces via conic bundles
Sho Tanimoto
Using the homological sieve method developed by Das--Lehmann--Tosteson and the author, we prove Peyre's all height approach to Manin's conjecture for split quintic del Pezzo surfac…
Intermediate Jacobians and Burnside invariants
Andrew Kresch, Sho Tanimoto, Yuri Tschinkel
We propose new invariants in equivariant birational geometry, combining equivariant intermediate Jacobians and the Burnside formalism, for smooth rationally connected threefolds wi…