R. Lodh

activity

20132026

collaborators

5 papers

math.AG2026

Toric flatness I

Rémi Lodh

We establish some basic properties of t-flat fine log schemes, i.e., fine log schemes whose underlying schemes are flat over their log structure (in a suitable sense). Notably, we…

math.AG2024

Cohomological flatness over discrete valuation rings: numerical and logarithmic criteria

Ofer Gabber, Rémi Lodh

We give sufficient conditions for cohomological flatness (in dimension 0) over discrete valuation rings, generalizing classical results of Raynaud in two different ways. The first…

math.NT2013

On Tate's conjecture for elliptic modular surfaces over finite fields

Rémi Lodh

For $N \geq 3$ , we show Tate's conjecture for the elliptic modular surface $E (N)$ of level $N$ over $F_{p}$ for a prime $p$ satisfying $p \equiv 1 mod N$ outside of a set of p…

math.NT2013

Almost étale extensions of Fontaine rings and log-crystalline cohomology in the semi-stable reduction case

Rémi Lodh

Let $K$ be a field of characteristic zero complete for a discrete valuation, with perfect residue field of characteristic $p > 0$ , and let $K^{+}$ be the valuation ring of $K$ . We rela…

math.NT2013

Bertini theorems for singular schemes and nearby cycles in mixed characteristic

Rémi Lodh

We first study hyperplane sections of some singular schemes over a field. We prove a Bertini theorem for the log smoothness of generic hyperplane sections of a large class of log s…