Zhang’s Conjecture and the Effective Bogomolov Conjecture over function fields

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Zhang’s Conjecture and the Effective Bogomolov Conjecture over Function Fields

We prove the Effective Bogomolov Conjecture, and so the Bogomolov Conjecture, over a function field of characteristic 0 by proving Zhang’s Conjecture about certain invariants of metrized graphs. In the function field case, these conjectures were previously known to be true only for curves of genus at most 4 and a few other special cases. We also either verify or improve the previous results. We...

متن کامل

Bogomolov Conjecture for Curves of Genus 2 over Function Fields

In this note, we will show that Bogomolov conjecture holds for a non-isotrivial curve of genus 2 over a function eld.

متن کامل

The Gross Conjecture over Rational Function Fields

We study the Gross Conjecture on the cyclotomic function field extension k(Λf )/k where k = Fq(t) is the rational function field and f is a monic polynomial in Fq[t]. We show the conjecture in the Fermat curve case(i.e., when f = t(t− 1)) by direct calculation. We also prove the case when f is irreducible which is analogous to Weil’s reciprocity law. In the general case, we manage to show the w...

متن کامل

Bogomolov Conjecture over Function Fields for Stable Curves with Only Irreducible Fibers

Let k be a field, X a smooth projective surface over k, Y a smooth projective curve over k, and f : X → Y a generically smooth semistable curve of genus g ≥ 2 over Y . Let K be the function field of Y , K the algebraic closure of K, and C the generic fiber of f . For D ∈ Pic(C)(K), let jD : CK → Pic 0(C)K be an embedding defined by jD(x) = x − D. Then, we have the following conjecture due to Bo...

متن کامل

Thomas ’ conjecture over Function Fields par

Thomas’ conjecture is, given monic polynomials p1, . . . , pd ∈ Z[a] with 0 < deg p1 < · · · < deg pd, then the Thue equation (over the rational integers) (X − p1(a)Y ) · · · (X − pd(a)Y ) + Y d = 1 has only trivial solutions, provided a ≥ a0 with effective computable a0. We consider a function field analogue of Thomas’ conjecture in case of degree d = 3. Moreover we find a counterexample to Th...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Inventiones mathematicae

سال: 2010

ISSN: 0020-9910,1432-1297

DOI: 10.1007/s00222-010-0282-7