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Tejasi Bhatnagar

Publications and source records attributed to Tejasi Bhatnagar.

5 recordsLinked to original sources
arXiv2026

Local monodromy of unit root F-isocrystals from Shimura varieties

We generalise a local $p$-adic monodromy theorem of Igusa that studies the monodromy representation associated to the universal elliptic curve around a supersingular point of the modular curve. Let $X$ be a smooth quasi-projective variety over $\mathbb{F}_p$. We set up and prove the analog of Igusa's theorem for overconvergent F-isocrystals on $X$ such that the action of the Frobenius is algebraic, $p$-plain, and semisimple at the closed points of $X$. We study the local monodromy of their unit root sub-objects around a point in $X$ with isoclinic Newton slopes. In particular, our result generalises Igusa's Theorem to overconvergent F-isocrystals arising from Shimura varieties, unconditionally for Shimura varieties of abelian type and conditional on Frobenius semisimplicity for exceptional Shimura varieties where this property is not known yet. In the particular case of Siegel Shimura varieties, we also prove an analogous result for the local monodromy of a point in the boundary of its compactification. As a consequence of our results, we prove a finiteness result for the reduction of the Hecke orbit of abelian varieties over a local field of equicharacteristic.

math.NT↗
arXiv2026

Covers of curves, Ceresa cycles, and Unlikely intersections

Fix a smooth, projective, geometrically integral curve $C$ of genus $g \geq 2$ over a characteristic zero field. We prove that the Ceresa cycle $\mathrm{Cer}(\widetilde{C})$ of a very general ramified cover $\widetilde{C}$ of $C$ is nontorsion in the Chow group of its Jacobian. We also show that there exist infinitely many families of ramified covers of a varying family of curves where a general point of these families corresponds to a curve with nontorsion Ceresa cycle. To illustrate this, we write down two explicit $1$-dimensional and $2$-dimensional families of genus $6$ curves where the locus of curves with torsion Ceresa cycle is Zariski closed and has positive codimension. Our strategy is to reduce the question of whether the Ceresa cycle is torsion to the question of whether a related point on the Jacobian of the curve is torsion. For this, we use the ``relative canonical shadow" of the Ceresa cycle, which is a point in the Jacobian of the curve obtained by intersecting the Ceresa cycle with a natural correspondence arising from the covering map. We combine this with ideas from unlikely intersection theory (namely the relative Manin--Mumford theorem) to study the locus where the relative canonical shadows of the Ceresa cycle become torsion.

math.AG↗
arXiv2024

Monodromy results for abelian surfaces and K3 surfaces with bad reduction

The purpose of this paper is to prove a local p-adic monodromy theorem for ordinary abelian surfaces and K3 surfaces with bad reduction in characteristic p. As an application, we get a finiteness result for the reduction of their Hecke orbits in the case of type II supersingular reduction.

math.NT↗
arXiv2024

Size of isogeny classes of abelian varieties of Lubin-Tate type

We prove a lower bound for the size of the isogeny class of a simple abelian variety over a finite field with commutative endomorphism ring in the Lubin-Tate case. Moreover, based on the expected size of the isogeny classes in the Newton stratum, we conjecture that this lower bound is sharp.

math.NT↗