Related papers: Cogalois theory and Drinfeld modules

We prove a uniqueness theorem for irreducible non-critical Gelfand-Tsetlin modules. The uniqueness result leads to a complete classification of the irreducible Gelfand-Tsetlin modules with 1-singularity. An explicit construction of such…

We classify all tilting classes over an arbitrary commutative ring via certain sequences of Thomason subsets of the spectrum, generalizing the classification for noetherian commutative rings by…

In representation theory of graded Iwanaga-Gorenstein algebras, tilting theory of the stable category $\underline{\mathsf{CM}}^{\mathbb{Z}} A$ of graded Cohen-Macaulay modules plays a prominent role. In this paper we study the following two…

Let $k$ be an algebraically closed field of characteristic $p>0$ and $G$ a finite group. We provide a description of the torsion subgroup $TT(G)$ of the finitely generated abelian group $T(G)$ of endo-trivial $kG$-modules when $p=2$ and $G$…

We show that a class of Dirichlet series ${\mathfrak{A}}^{\#}$ that is much larger than the extended Selberg class ${\mathscr{S}}^{\#}$, and also contains the standard as well as the tensor product, exterior square and symmetric square…

We develop silting theory of a noetherian algebra $\Lambda$ over a commutative noetherian ring $R$. We study mutation theory of $2$-term silting complexes of $\Lambda$, and as a consequence, we see that mutation exists. As in the case of…

In this paper, we study the Galois representations attached to products of Drinfeld modules. As an analogue of Serre's classical result on the images of Galois representations associated with products of elliptic curves, we prove that for…

The well-known Chowla and Zassenhaus conjecture, proven by Cohen in 1990, states that for any $d\ge 2$ and any prime $p>(d^2-3d+4)^2$ there is no complete mapping polynomial in $\mathbb{F}_{p}[x]$ of degree $d$. For arbitrary finite fields…

We complete the proof of a Siegel type statement for finitely generated $\Phi$-submodules of $\mathbb{G}_a$ under the action of a Drinfeld module $\Phi$.

Enochs Conjecture asserts that each covering class of modules (over any ring) has to be closed under direct limits. Although various special cases of the conjecture have been verified, the conjecture remains open in its full generality. In…

We disprove, by means of numerical examples, the existence of a Riemann-Hurwitz formula for the p-ranks of relative class groups in a p-ramified p-extension K/k of number fields of CM-type containing ?\_p. In the cyclic case of degree p,…

This continues recent work in a paper by Corner, Gobel and Goldsmith. A particular question was left open: Is it possible to carry over the results concerning the undecidability of torsion--free Crawley groups to modules over the ring of…

The Coleman-Mandula (CM) theorem states that the Poincar\'e and internal symmetries of a Minkowski spacetime quantum field theory cannot combine nontrivially in an extended symmetry group. We establish an analogous result for quantum field…

What is the true order of growth of torsion in the cohomology of an arithmetic group? Let $D$ be a quaternion over an imaginary quadratic field $F.$ Let $E/F$ be a cyclic Galois extension with $\mathrm{Gal}(E/F) = \langle \sigma \rangle.$…

When travelling from the number fields theory to the function fields theory, one cannot miss the deep analogy between rank 1 Drinfeld modules and the group of root of unity and the analogy between rank 2 Drinfeld modules and elliptic…

If E is a non-isotrivial elliptic curve over a global function field F of odd characteristic we show that certain Mordell-Weil groups of E have 1-dimensional eigenspace relative to a fixed complex ring class character provided that the…

We develop a Galois theory for difference ring extensions, inspired by Magid's separable Galois theory for ring extensions and by Janelidze's categorical Galois theory. Our difference Galois theorem states that the category of difference…

We prove very general index formulae for integral Galois modules, specifically for units in rings of integers of number fields, for higher K-groups of rings of integers, and for Mordell-Weil groups of elliptic curves over number fields.…

In this paper we investigate a local to global principle for Mordell-Weil group defined over a ring of integers ${\cal O}_K$ of $t$-modules that are products of the Drinfeld modules ${\widehat\varphi}={\phi}_{1}^{e_1}\times \dots \times…

In this paper, a strong multiplicity one theorem for Katz modular forms is studied. We show that a cuspidal Katz eigenform which admits an irreducible Galois representation is in the level and weight old space of a uniquely associated Katz…