diff --git a/Arithmetic_kernel/include/CGAL/BOOST_MP_arithmetic_kernel.h b/Arithmetic_kernel/include/CGAL/BOOST_MP_arithmetic_kernel.h
new file mode 100644
index 00000000000..101ee85e4c4
--- /dev/null
+++ b/Arithmetic_kernel/include/CGAL/BOOST_MP_arithmetic_kernel.h
@@ -0,0 +1,45 @@
+// Copyright (c) 2017 Inria.
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public License as
+// published by the Free Software Foundation; either version 3 of the License,
+// or (at your option) any later version.
+//
+// Licensees holding a valid commercial license may use this file in
+// accordance with the commercial license agreement provided with the software.
+//
+// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
+// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+//
+// Author: Marc Glisse <marc.glisse@inria.fr>
+
+#ifndef CGAL_GMPXX_ARITHMETIC_KERNEL_H
+#define CGAL_GMPXX_ARITHMETIC_KERNEL_H
+
+#include <CGAL/Arithmetic_kernel/Arithmetic_kernel_base.h>
+#include <CGAL/Get_arithmetic_kernel.h>
+
+#include <CGAL/boost_mp.h>
+
+// FIXME: the could be several kernels based on Boost.Multiprecision.
+
+namespace CGAL {
+/** \ingroup CGAL_Arithmetic_kernel
+ *  \brief The Boost.Multiprecision set of exact number types
+ */
+struct BOOST_MP_arithmetic_kernel : internal::Arithmetic_kernel_base {
+  typedef boost::multiprecision::cpp_int Integer;
+  typedef boost::multiprecision::cpp_rational Rational;
+};
+
+template <class B1, boost::multiprecision::expression_template_option E1>
+struct Get_arithmetic_kernel<boost::multiprecision::number<B1, E1> > {
+  typedef BOOST_MP_arithmetic_kernel Arithmetic_kernel;
+};
+template <class T1, class T2, class T3, class T4, class T5>
+struct Get_arithmetic_kernel<boost::multiprecision::detail::expression<T1,T2,T3,T4,T5> > {
+  typedef BOOST_MP_arithmetic_kernel Arithmetic_kernel;
+};
+} //namespace CGAL
+#endif
diff --git a/Number_types/include/CGAL/boost_mp.h b/Number_types/include/CGAL/boost_mp.h
index a0dcabffc08..9b92356d472 100644
--- a/Number_types/include/CGAL/boost_mp.h
+++ b/Number_types/include/CGAL/boost_mp.h
@@ -359,6 +359,21 @@ struct Coercion_traits<boost::multiprecision::number<B1, E1>, boost::multiprecis
       }
   };
 };
+// Avoid ambiguity with the specialization for <A,A> ...
+template <class B1, boost::multiprecision::expression_template_option E1>
+struct Coercion_traits<boost::multiprecision::number<B1, E1>, boost::multiprecision::number<B1, E1> >
+{
+  typedef boost::multiprecision::number<B1, E1> Type;
+  typedef Tag_true Are_implicit_interoperable;
+  typedef Tag_true Are_explicit_interoperable;
+  struct Cast{
+    typedef Type result_type;
+    template <class U>
+      Type operator()(const U& x) const {
+	return Type(x);
+      }
+  };
+};
 
 template <class T1, class T2, class T3, class T4, class T5, class U1, class U2, class U3, class U4, class U5>
 struct Coercion_traits <
@@ -368,6 +383,15 @@ boost::multiprecision::detail::expression<U1,U2,U3,U4,U5> >
 typename boost::multiprecision::detail::expression<T1,T2,T3,T4,T5>::result_type,
 typename boost::multiprecision::detail::expression<U1,U2,U3,U4,U5>::result_type>
 { };
+// Avoid ambiguity with the specialization for <A,A> ...
+template <class T1, class T2, class T3, class T4, class T5>
+struct Coercion_traits <
+boost::multiprecision::detail::expression<T1,T2,T3,T4,T5>,
+boost::multiprecision::detail::expression<T1,T2,T3,T4,T5> >
+: Coercion_traits <
+typename boost::multiprecision::detail::expression<T1,T2,T3,T4,T5>::result_type,
+typename boost::multiprecision::detail::expression<T1,T2,T3,T4,T5>::result_type>
+{ };
 
 template <class B, boost::multiprecision::expression_template_option E, class T1, class T2, class T3, class T4, class T5>
 struct Coercion_traits<boost::multiprecision::number<B, E>, boost::multiprecision::detail::expression<T1,T2,T3,T4,T5> >
@@ -383,10 +407,55 @@ typename boost::multiprecision::detail::expression<T1,T2,T3,T4,T5>::result_type,
 boost::multiprecision::number<B, E> >
 { };
 
-// TODO: coercion with int, long, double...
+// TODO: coercion with expressions, fix existing coercions
 // (double -> rational is implicit only for 1.56+, see ticket #10082)
+// The real solution would be to avoid specializing Coercion_traits for all pairs of number types and let it auto-detect what works, so only broken types need an explicit specialization.
+
+// Ignore types smaller than long
+#define CGAL_COERCE_INT(int) \
+template <class B1, boost::multiprecision::expression_template_option E1> \
+struct Coercion_traits<boost::multiprecision::number<B1, E1>, int> { \
+  typedef boost::multiprecision::number<B1, E1> Type; \
+  typedef Tag_true Are_implicit_interoperable; \
+  typedef Tag_true Are_explicit_interoperable; \
+  struct Cast{ \
+    typedef Type result_type; \
+    template <class U> Type operator()(const U& x) const { return Type(x); } \
+  }; \
+}; \
+template <class B1, boost::multiprecision::expression_template_option E1> \
+struct Coercion_traits<int, boost::multiprecision::number<B1, E1> > \
+: Coercion_traits<boost::multiprecision::number<B1, E1>, int> {}
+
+CGAL_COERCE_INT(short);
+CGAL_COERCE_INT(int);
+CGAL_COERCE_INT(long);
+#undef CGAL_COERCE_INT
+
+// Ignore bounded-precision rationals
+#define CGAL_COERCE_FLOAT(float) \
+template <class B1, boost::multiprecision::expression_template_option E1> \
+struct Coercion_traits<boost::multiprecision::number<B1, E1>, float> { \
+  typedef boost::multiprecision::number<B1, E1> Type; \
+  typedef Boolean_tag<boost::multiprecision::number_category<Type>::value != boost::multiprecision::number_kind_integer> Are_implicit_interoperable; \
+  typedef Are_implicit_interoperable Are_explicit_interoperable; \
+  struct Cast{ \
+    typedef Type result_type; \
+    template <class U> Type operator()(const U& x) const { return Type(x); } \
+  }; \
+}; \
+template <class B1, boost::multiprecision::expression_template_option E1> \
+struct Coercion_traits<float, boost::multiprecision::number<B1, E1> > \
+: Coercion_traits<boost::multiprecision::number<B1, E1>, float> {}
+
+CGAL_COERCE_FLOAT(float);
+CGAL_COERCE_FLOAT(double);
+#undef CGAL_COERCE_FLOAT
+
 
 } //namespace CGAL
 
+#include <CGAL/BOOST_MP_arithmetic_kernel.h>
+
 #endif // BOOST_VERSION
 #endif