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Creators/Authors contains: "Harbater, David"

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  1. ; ; (, Israel Journal of Mathematics)
    We provide a uniform bound for the index of cohomology classes over semiglobal fields (i.e., over one-variable function fields over a complete discretely valued field K). The bound is given in terms of the analogous data for the residue field of K and its finitely generated extensions of transcendence degree at most one. We also obtain analogous bounds for collections of cohomology classes. Our results provide recursive formulas for function fields over higher rank complete discretely valued fields, and explicit bounds in some cases when the information on the residue field is known. In the process, we prove a splitting result for cohomology classes of degree 3 in the context of surfaces over finite fields. ∗ 
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  2. ; ; ; ; ; (, Michigan Mathematical Journal)
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  3. (, Albanian journal of mathematics)
    Double coset spaces of adelic points on linear algebraic groups arise in the study of global fields; e.g., concerning local-global principles and torsors. A different type of double coset space plays a role in the study of semi-global fields such as p-adic function fields. This paper relates the two, by establishing adelic double coset spaces over semi-global fields; relating them to local-global principles and torsors; and providing explicit examples. 
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  4. ; ; ; (, Transactions of the American Mathematical Society)
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  5. ; ; ; (, Advances in Mathematics)
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  6. ; ; ; ; ; (, Algebraic Geometry)
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  7. ; ; ; (, Journal of the Institute of Mathematics of Jussieu)
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    We solve the inverse differential Galois problem over differential fields with a large field of constants of infinite transcendence degree over  $$\mathbb{Q}$$ . More generally, we show that over such a field, every split differential embedding problem can be solved. In particular, we solve the inverse differential Galois problem and all split differential embedding problems over $$\mathbb{Q}_{p}(x)$$ . 
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  8. ; ; (, Journal of Algebra)
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  9. ; ; (, Bulletin of the London Mathematical Society)