A first-order theory has the Schröder-Bernstein Property if any two of its models that are elementarily bi-embeddable are isomorphic. We prove (as Theorem 3.8): Theorem 1. If G is an abelian group, then the following are equivalent: 1. Th(G,+) has the Schröder-Bernstein property; 2. Th(G,+) is ω-stable; 3. G is the direct sum of a divisible group and a torsion group of

We generalize purity of the Newton stratification to purity for a single break point of the Newton point in the context of local G-shtukas respectively of elements of the loop group of a reductive group. As an application we prove that elements of the loop group bounded by a given dominant coweight satisfy a generalization of Grothendieck’s conjecture on deformations of p-divisible groups with ...

It is known that the number of homomorphisms from a group $F$ to $G$ divisible by greatest common divisor order and exponent $F/[F,F]$. We investigate satisfying some natural conditions such as injectivity or surjectivity. The simplest nontrivial corollary our results following fact: {\it in any finite group, generating pairs $(x,y)$ $x^3=1=y^5$, multiple 15 $[G,G]\cdot\{g^{15}\;|\;g\in G\}$.

Abstract Given a Henselian valuation, we study its definability (with and without parameters) by examining conditions on the value group. We show that any valuation whose group is not closed in divisible hull definable language of rings, using one parameter. Thereby strengthen known results. Moreover, this case, parameter optimal sense cannot obtain parameters. To end, present construction meth...

Let F be a nonarchimedean local field of characteristic 0 and residue order not divisible by 2. We show how to calculate the product covolume torsion-free lattice in PGL(2,F) formal dimension discrete series representation GL(2,F). The comes from theorem Ihara, dimensions are contained results Corwin, Moy, Sally. By going back Atiyah, triviality second cohomology group free group, resulting is ...