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10 papers · 1 filter
Algebraic independence of arithmetic gamma values and Carlitz zeta values
Chieh-Yu Chang, Matthew A. Papanikolas, Dinesh S. Thakur +1
We consider the values at proper fractions of the arithmetic gamma function and the values at positive integers of the zeta function for F_q[theta] and provide complete algebraic i…
Ray Class Groups of Quadratic and Cyclotomic Fields
Jing Long Hoelscher
This paper studies Galois extensions over real quadratic number fields or cyclotomic number fields ramified only at one prime. In both cases, the ray class groups are computed, and…
Infinite class field towers
Jing Long Hoelscher
This paper studies infinite class field towers of number fields that are ramified over $\Q$ only at one finite prime. In particular, we show the existence of such towers for a…
Galois extensions ramified only at one prime
Jing Long Hoelscher
This paper gives some restrictions on finite groups that can occur as Galois groups of extensions over $\Q$ and over $\F_q(t)$ ramified only at one finite prime. Over $\Q$, we stre…
Jacobi sums, Fermat Jacobians, and ranks of abelian varieties over towers of function fields
Douglas Ulmer
Our goal in this note is to give a number of examples of abelian varieties over function fields k(t) which have bounded ranks in towers of extensions such as k(t^{1/d}) for varying…
On two theorems for flat, affine group schemes over a discrete valuation ring
Adrian Vasiu
We include short and elementary proofs of two theorems characterizing reductive group schemes over a discrete valuation ring, in a slightly more general context.