Mihran Papikian

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math.NT2011

$D$ -elliptic sheaves and odd Jacobians

Mihran Papikian

We examine the existence of rational divisors on modular curves of $D$ -elliptic sheaves and on Atkin-Lehner quotients of these curves over local fields. Using a criterion…

math.NT2011

On Jacquet-Langlands isogeny over function fields

Mihran Papikian

We propose a conjectural explicit isogeny from the Jacobians of hyperelliptic Drinfeld modular curves to the Jacobians of hyperelliptic modular curves of $D$ -elliptic she…

math.NT2010

On generators of arithmetic groups over function fields

Mihran Papikian

Let $F = F_{q} (T)$ be the field of rational functions with $F_{q}$ -coefficients, and $A = F_{q} [T]$ be the subring of polynomials. Let $D$ be a division quaternion…

math.NT2010

Local diophantine properties of modular curves of $D$ -elliptic sheaves

Mihran Papikian

We study the existence of rational points on modular curves of $D$ -elliptic sheaves over local fields and the structure of special fibres of these curves. We discuss some app…

math.NT2010

On finite arithmetic simplicial complexes

Mihran Papikian

We compute the Euler-Poincaré characteristic of quotients of the Bruhat-Tits building of PGL(n) under the action of arithmetic groups arising from central division algebras over ra…

D-elliptic sheaves and odd Jacobians

On Jacquet-Langlands isogeny over function fields

On generators of arithmetic groups over function fields

Local diophantine properties of modular curves of D-elliptic sheaves

On finite arithmetic simplicial complexes

$D$ -elliptic sheaves and odd Jacobians

Local diophantine properties of modular curves of $D$ -elliptic sheaves